{"id":5714,"date":"2026-07-05T12:01:06","date_gmt":"2026-07-05T03:01:06","guid":{"rendered":"https:\/\/www.ktech.biz\/jp\/?p=5714"},"modified":"2026-07-05T12:08:01","modified_gmt":"2026-07-05T03:08:01","slug":"10-4_ode","status":"publish","type":"post","link":"https:\/\/www.ktech.biz\/jp\/num\/10-4_ode\/","title":{"rendered":"10.4 \u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u5b9f\u7528\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u30d9\u30f3\u30c1\u30de\u30fc\u30af"},"content":{"rendered":"\n<h3>10.4.1 \u5b9f\u7528\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u9078\u629e<\/h3>\n<p>XLPack \u306b\u53ce\u9332\u3055\u308c\u3066\u3044\u308b\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u7528\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u306f\u3059\u3079\u3066\u30b9\u30c6\u30c3\u30d7\u5e45\u81ea\u52d5\u8abf\u7bc0\u6a5f\u80fd\u3092\u6301\u3063\u3066\u3044\u308b. \u5bc6\u51fa\u529b\u306e\u5fc5\u8981\u6027\u306a\u3069\u3092\u53c2\u8003\u306b\u4f7f\u7528\u3059\u308b\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u9078\u629e\u3059\u308b\u3068\u3088\u3044. \u306a\u304a, \u30b9\u30c6\u30a3\u30d5\u306a\u554f\u984c\u7528\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u30b9\u30c6\u30a3\u30d5\u3067\u306f\u306a\u3044\u554f\u984c\u306b\u4f7f\u7528\u3057\u3066\u3082\u89e3\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u304c\u52b9\u7387\u306f\u60aa\u304f\u306a\u308b.<\/p>\n<h3>XLPack \u306b\u53ce\u9332\u3055\u308c\u3066\u3044\u308b\u30d7\u30ed\u30b0\u30e9\u30e0 (\u30b9\u30c6\u30a3\u30d5\u3067\u306f\u306a\u3044\u554f\u984c\u7528)<\/h3>\n<div class=\"su-table su-table-responsive su-table-alternate\">\n<table>\n<tbody>\n<tr>\n<th>\u30d7\u30ed\u30b0\u30e9\u30e0\u540d<\/th>\n<th>\u89e3\u6cd5<\/th>\n<th>\u30b9\u30c6\u30c3\u30d7\u5e45\u81ea\u52d5\u8abf\u7bc0<\/th>\n<th>\u5bc6\u51fa\u529b<\/th>\n<th>\u7279\u8a18\u4e8b\u9805<\/th>\n<\/tr>\n<tr>\n<td>Derkfa<\/td>\n<td>5(4) \u6b21 \u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u30fb\u30d5\u30a7\u30fc\u30eb\u30d9\u30eb\u30b0\u6cd5<\/td>\n<td>\u3007<\/td>\n<td>\u3007<\/td>\n<td>RKF45 \u3068\u540c\u7b49<\/td>\n<\/tr>\n<tr>\n<td>Dopri5a<\/td>\n<td>5(4) \u6b21 \u30c9\u30eb\u30de\u30f3\u30fb\u30d7\u30ea\u30f3\u30b9\u6cd5<\/td>\n<td>\u3007<\/td>\n<td>\u3007<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Dverka<\/td>\n<td>6(5) \u6b21 \u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u30fb\u30f4\u30a1\u30fc\u30ca\u30fc\u6cd5<\/td>\n<td>\u3007<\/td>\n<td>\u3007<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Dop853a<\/td>\n<td>8(5,3) \u6b21 \u30c9\u30eb\u30de\u30f3\u30fb\u30d7\u30ea\u30f3\u30b9\u6cd5<\/td>\n<td>\u3007<\/td>\n<td>\u3007<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Deabm<\/td>\n<td>1\u301c12 \u53ef\u5909\u6b21\u6570 \u30a2\u30c0\u30e0\u30b9\u30fb\u30d0\u30b7\u30e5\u30d5\u30a9\u30fc\u30b9\u30fb\u30e0\u30eb\u30c8\u30f3\u6cd5<\/td>\n<td>\u3007<\/td>\n<td>\u203b2<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Odex<\/td>\n<td>\u88dc\u5916\u6cd5 (GBS \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0)<\/td>\n<td>\u3007<\/td>\n<td>\u3007<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Retard<\/td>\n<td>5(4) \u6b21 \u30c9\u30eb\u30de\u30f3\u30fb\u30d7\u30ea\u30f3\u30b9\u6cd5<\/td>\n<td>\u3007<\/td>\n<td>\u3007<\/td>\n<td>\u9045\u5ef6\u5fae\u5206\u65b9\u7a0b\u5f0f (DDE) \u7528<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\u203b1 \u305d\u308c\u305e\u308c\u306e\u30ea\u30d0\u30fc\u30b9\u30b3\u30df\u30e5\u30cb\u30b1\u30fc\u30b7\u30e7\u30f3\u7248\u3082\u4f7f\u7528\u53ef\u80fd(\u30eb\u30fc\u30c1\u30f3\u540d\u306b&#8221;_r&#8221;\u306e\u30b5\u30d5\u30a3\u30c3\u30af\u30b9\u304c\u4ed8\u304f).<br \/>\n\u203b2 Deabm \u3067\u306f\u6307\u5b9a\u3057\u306a\u3044\u9650\u308a\u88dc\u9593\u5024\u304c\u4f7f\u7528\u3067\u304d\u308c\u3070\u305d\u308c\u3092\u4f7f\u7528\u3059\u308b.<\/p>\n<h3>XLPack \u306b\u53ce\u9332\u3055\u308c\u3066\u3044\u308b\u30d7\u30ed\u30b0\u30e9\u30e0 (\u30b9\u30c6\u30a3\u30d5\u3067\u306f\u306a\u3044 2 \u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (y&#8221; = f(t, y)) \u7528)<\/h3>\n<div class=\"su-table su-table-responsive su-table-alternate\">\n<table>\n<tbody>\n<tr>\n<th>\u30d7\u30ed\u30b0\u30e9\u30e0\u540d<\/th>\n<th>\u89e3\u6cd5<\/th>\n<th>\u30b9\u30c6\u30c3\u30d7\u5e45\u81ea\u52d5\u8abf\u7bc0<\/th>\n<th>\u5bc6\u51fa\u529b<\/th>\n<th>\u7279\u8a18\u4e8b\u9805<\/th>\n<\/tr>\n<tr>\n<td>Dopn43<\/td>\n<td>4(3) \u6b21\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u30fb\u30cb\u30e5\u30b9\u30c8\u30ec\u30e0\u6cd5<\/td>\n<td>\u3007<\/td>\n<td>\u3007<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Dopn64<\/td>\n<td>6(4) \u6b21\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u30fb\u30cb\u30e5\u30b9\u30c8\u30ec\u30e0\u6cd5<\/td>\n<td>\u3007<\/td>\n<td>\u3007<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Dopn86<\/td>\n<td>8(6) \u6b21\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u30fb\u30cb\u30e5\u30b9\u30c8\u30ec\u30e0\u6cd5<\/td>\n<td>\u3007<\/td>\n<td>\u3007<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Dopn1210<\/td>\n<td>12(10) \u6b21\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u30fb\u30cb\u30e5\u30b9\u30c8\u30ec\u30e0\u6cd5<\/td>\n<td>\u3007<\/td>\n<td>\u00d7<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Odex2<\/td>\n<td>\u88dc\u5916\u6cd5 (GBS \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0)<\/td>\n<td>\u3007<\/td>\n<td>\u3007<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\u203b1 \u305d\u308c\u305e\u308c\u306e\u30ea\u30d0\u30fc\u30b9\u30b3\u30df\u30e5\u30cb\u30b1\u30fc\u30b7\u30e7\u30f3\u7248\u3082\u4f7f\u7528\u53ef\u80fd(\u30eb\u30fc\u30c1\u30f3\u540d\u306b&#8221;_r&#8221;\u306e\u30b5\u30d5\u30a3\u30c3\u30af\u30b9\u304c\u4ed8\u304f)<\/p>\n<h3>XLPack \u306b\u53ce\u9332\u3055\u308c\u3066\u3044\u308b\u30d7\u30ed\u30b0\u30e9\u30e0 (\u30b9\u30c6\u30a3\u30d5\u306a\u554f\u984c\u7528)<\/h3>\n<div class=\"su-table su-table-responsive su-table-alternate\">\n<table>\n<tbody>\n<tr>\n<th>\u30d7\u30ed\u30b0\u30e9\u30e0\u540d<\/th>\n<th>\u89e3\u6cd5<\/th>\n<th>\u30b9\u30c6\u30c3\u30d7\u5e45\u81ea\u52d5\u8abf\u7bc0<\/th>\n<th>\u5bc6\u51fa\u529b<\/th>\n<th>\u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f(DAE)\u306b\u4f7f\u7528\u53ef<\/th>\n<th>\u7279\u8a18\u4e8b\u9805<\/th>\n<\/tr>\n<tr>\n<td>Debdf<\/td>\n<td>1 \u301c 5 \u6b21 \u5f8c\u9000\u5fae\u5206\u516c\u5f0f (BDF)<\/td>\n<td>\u3007<\/td>\n<td>\u203b2<\/td>\n<td>\u00d7<\/td>\n<td>LSODE \u3068\u540c\u7b49<\/td>\n<\/tr>\n<tr>\n<td>Radaua<\/td>\n<td>5, 9, 13 \u6b21\u306e\u9670\u7684\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5 (\u30e9\u30c0\u30a6 IIA \u6cd5)<\/td>\n<td>\u3007<\/td>\n<td>\u3007<\/td>\n<td>My&#8217; = f(t, y) \u6307\u6570 3 \u4ee5\u4e0b<\/td>\n<td>\u6b21\u6570\u3092\u6307\u5b9a\u307e\u305f\u306f\u81ea\u52d5\u9078\u629e\u53ef\u80fd<\/td>\n<\/tr>\n<tr>\n<td>Rodasa<\/td>\n<td>4(3) \u6b21 \u30ed\u30fc\u30bc\u30f3\u30d6\u30ed\u30c3\u30af\u6cd5<\/td>\n<td>\u3007<\/td>\n<td>\u3007<\/td>\n<td>My&#8217; = f(t, y) \u6307\u6570 1<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Seulex<\/td>\n<td>\u88dc\u5916\u6cd5 (\u7dda\u5f62\u9670\u7684\u30aa\u30a4\u30e9\u30fc\u6cd5)<\/td>\n<td>\u3007<\/td>\n<td>\u3007<\/td>\n<td>My&#8217; = f(t, y) \u6307\u6570 1<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\u203b1 \u305d\u308c\u305e\u308c\u306e\u30ea\u30d0\u30fc\u30b9\u30b3\u30df\u30e5\u30cb\u30b1\u30fc\u30b7\u30e7\u30f3\u7248\u3082\u4f7f\u7528\u53ef\u80fd(\u30eb\u30fc\u30c1\u30f3\u540d\u306b&#8221;_r&#8221;\u306e\u30b5\u30d5\u30a3\u30c3\u30af\u30b9\u304c\u4ed8\u304f)<br \/>\n\u203b2 Debdf \u3067\u306f\u6307\u5b9a\u3057\u306a\u3044\u9650\u308a\u88dc\u9593\u5024\u304c\u4f7f\u7528\u3067\u304d\u308c\u3070\u305d\u308c\u3092\u4f7f\u7528\u3059\u308b.<\/p>\n<h3>10.4.2 \u30b9\u30c6\u30a3\u30d5\u3067\u306a\u3044\u554f\u984c<\/h3>\n<p>\u672c\u7bc0\u306e\u4f8b\u984c\u306e\u8a73\u7d30\u306f\u53c2\u8003\u6587\u732e[5]\u3092\u53c2\u7167\u306e\u3053\u3068.<\/p>\n<p>\u3053\u3053\u3067\u306f\u95a2\u6570\u306e\u547c\u3073\u51fa\u3057\u56de\u6570\u3067\u3057\u304b\u8a55\u4fa1\u3057\u3066\u3044\u306a\u3044\u304c, \u7dcf\u3058\u3066, \u9ad8\u7cbe\u5ea6\u516c\u5f0f\u3092\u4f7f\u3063\u3066\u3044\u308b Dop853a \u3068\u30a2\u30c0\u30e0\u30b9\u30fb\u30d0\u30b7\u30e5\u30d5\u30a9\u30fc\u30b9\u30fb\u30e2\u30eb\u30c8\u30f3\u6cd5\u306e Deabm \u304c\u901f\u3044. \u307e\u305f, \u88dc\u5916\u6cd5\u306e Odex \u3082\u60aa\u304f\u306a\u3044. \u30b9\u30c6\u30c3\u30d7\u5e45\u306e\u5236\u5fa1\u6a5f\u80fd\u3092\u6301\u305f\u306a\u3044\u901a\u5e38\u306e\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5\u3082\u6bd4\u8f03\u3057\u305f\u304c\u95a2\u6570\u306e\u5909\u5316\u304c\u6fc0\u3057\u3044\u5b9f\u8df5\u554f\u984c\u3067\u306f\u82e6\u3057\u3044\u3088\u3046\u3067\u3042\u308b.<\/p>\n<h4>(1) \u525b\u4f53\u306e\u56de\u8ee2\u306b\u5bfe\u3059\u308b\u30aa\u30a4\u30e9\u30fc\u65b9\u7a0b\u5f0f<\/h4>\n<p>\u525b\u4f53\u306e\u56de\u8ee2\u306b\u5bfe\u3059\u308b\u30aa\u30a4\u30e9\u30fc\u65b9\u7a0b\u5f0f\u306f\u6b21\u306e\u3068\u304a\u308a.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&#038; I_1y_1&#8242; = (I_2 &#8211; I_3)y_2y_3 \\\\<br \/>\n&#038; I_2y_2&#8242; = (I_3 &#8211; I_1)y_3y_1 \\\\<br \/>\n&#038; I_3y_3&#8242; = (I_1 &#8211; I_2)y_1y_2 + f(x) \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\\(y_1, y_2, y_3\\) \u306f\u56de\u8ee2\u30d9\u30af\u30c8\u30eb\u306e\u5ea7\u6a19, \\(I_1, I_2, I_3\\) \u306f\u4e3b\u6163\u6027\u30e2\u30fc\u30e1\u30f3\u30c8\u3067\u3042\u308b. \u7b2c 3 \u5ea7\u6a19\u306b\u306f\u6b21\u306e\u5916\u90e8\u5f37\u5236\u529b\u304c\u52a0\u308f\u3063\u3066\u3044\u308b.<br \/>\n\\[<br \/>\n\\begin{equation}<br \/>\nf(x) =<br \/>\n\\begin{cases}<br \/>\n0.25 sin^2x &#038; (3\\pi \\le x \\le 4\\pi) \\\\<br \/>\n0 &#038; (\u305d\u306e\u4ed6\u306e x) \\\\<br \/>\n\\end{cases}<br \/>\n\\end{equation}<br \/>\n\\]\n\u521d\u671f\u5024\u306f \\(I_1 = 0.5, \\space I_2 = 2, \\space I_3 = 3, \\space y_1(0) = 1, \\space y_2(0) = 0, \\space y_3(0) = 0.9\\) \u3067\u3042\u308b.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_1_exp1.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5731\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_1_exp1.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_1_exp1-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>\u3053\u308c\u3092, Derkfa, Dopri5a, Dverka, Dop853a, Deabm \u304a\u3088\u3073 Odexa \u3092\u7528\u3044\u3066 \\(Tol \\space (\u8981\u6c42\u7cbe\u5ea6) = 10^{-6}, 10^{-7}, \\dots, 10^{-15}\\) \u3068\u5909\u5316\u3055\u305b\u3066\u8a08\u7b97\u3057\u305f. \u6bd4\u8f03\u306e\u305f\u3081\u30aa\u30a4\u30e9\u30fc\u6cd5 (Euler) \u3068 4 \u6b21\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5 (RK4) \u3082\u8868\u793a\u3057\u305f. \u3053\u3061\u3089\u306f \\(h = 0.01, \\space 0.005, \\space \\dots, \\space 10^{-5}\\) \u3068\u5909\u5316\u3055\u305b\u3066\u8a08\u7b97\u3057\u305f.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_2_exp1_2.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5732\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_2_exp1_2.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_2_exp1_2-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>x \u8ef8\u306f t = 20 \u306b\u304a\u3051\u308b \\(y_1, \\space y_2, \\space y_3\\) \u306e\u76f8\u5bfe\u8aa4\u5dee\u306e\u5e73\u5747\u3067, \u53f3\u306b\u3044\u304f\u307b\u3069\u5c0f\u3055\u3044 (\u7cbe\u5ea6\u304c\u3088\u3044).\u3000y \u8ef8\u306f\u305d\u306e\u3068\u304d\u306e\u95a2\u6570\u8a55\u4fa1\u56de\u6570\u3067\u3042\u308b. \u4e21\u8ef8\u3068\u3082\u5bfe\u6570\u76ee\u76db\u3067\u30d7\u30ed\u30c3\u30c8\u3057\u305f.<\/p>\n<p>\u4ed6\u306e\u554f\u984c\u3067\u3082\u305d\u3046\u3067\u3042\u308b\u304c, \\(Tol = 10^{-13}, 10^{-14}, 10^{-15}\\) \u306a\u3069\u306f\u904e\u5270\u306a\u8981\u6c42\u3060\u3068\u601d\u308f\u308c, \u3042\u308b\u7a0b\u5ea6\u306e\u3068\u3053\u308d\u304b\u3089\u306f\u7d50\u679c\u306e\u7cbe\u5ea6\u306f\u4e0a\u304c\u3089\u306a\u3044. \u30d7\u30ed\u30b0\u30e9\u30e0\u306b\u3088\u3063\u3066\u9014\u4e2d\u3067\u8a08\u7b97\u3092\u7d42\u4e86\u3059\u308b\u3082\u306e\u3068\u69cb\u308f\u305a\u8a08\u7b97\u3092\u7d9a\u3051\u308b\u3082\u306e\u304c\u3042\u308b.<\/p>\n<p>\u3053\u306e\u554f\u984c\u306f 4 \u6b21\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5\u306f\u5c11\u3057\u5909\u306a\u52d5\u304d\u3092\u793a\u3057\u3066\u3044\u308b\u304c\u7cbe\u5ea6 \\(10^{-11}\\) \u4ed8\u8fd1\u307e\u3067\u306f\u554f\u984c\u306a\u304f\u8a08\u7b97\u3067\u304d\u3066\u3044\u308b. \u30aa\u30a4\u30e9\u30fc\u6cd5\u3067\u3082\u30b9\u30c6\u30c3\u30d7\u5e45\u3092\u5c0f\u3055\u304f\u3057\u3066\u3044\u3051\u3070\u6b63\u3057\u304f\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u3067\u3042\u308b\u304c, \u6642\u9593\u304c\u304b\u304b\u308a\u3059\u304e\u308b (\u95a2\u6570\u8a55\u4fa1\u56de\u6570\u304c\u591a\u3059\u304e\u308b).<\/p>\n<h4>(2) \u30ed\u30fc\u30ec\u30f3\u30c4\u65b9\u7a0b\u5f0f<\/h4>\n<p>\u30ed\u30fc\u30ec\u30f3\u30c4\u65b9\u7a0b\u5f0f\u306f\u30ab\u30aa\u30b9\u7684\u3075\u308b\u307e\u3044\u3092\u3059\u308b\u65b9\u7a0b\u5f0f\u3067\u3042\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&#038; y_1&#8242; = -\\sigma y_1 + \\sigma y_2 \\\\<br \/>\n&#038; y_2&#8242; = -y_1y_3 + ry_1 &#8211; y_2 \\\\<br \/>\n&#038; y_3&#8242; = y_1y_2 &#8211; by_3 \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\u30b6\u30eb\u30c4\u30de\u30f3\u306e\u5024 \\(\\sigma = 10, \\space r = 28, \\space b = 8\/3\\) \u3092\u4f7f\u3046\u3068\u975e\u5468\u671f\u7684\u306b\u306a\u308b. \u521d\u671f\u5024\u3092 \\(y_1(0) = -8, \\space y_2(0) = 8, \\space y_3(0) = 27\\) \u3068\u3057\u3066\u8a08\u7b97\u3059\u308b\u3068\u6b21\u306e\u3088\u3046\u306a\u30ed\u30fc\u30ec\u30f3\u30c4\u30fb\u30a2\u30c8\u30e9\u30af\u30bf\u3068\u3088\u3070\u308c\u308b\u56f3\u5f62\u304c\u5f97\u3089\u308c\u308b.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_3_exp2.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5733\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_3_exp2.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_3_exp2-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_4_exp2_2.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5734\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_4_exp2_2.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_4_exp2_2-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>\u4e0a\u3068\u540c\u69d8\u306b, Derkfa, Dopri5a, Dverka, Dop853a, Deabm \u304a\u3088\u3073 Odexa \u3092\u7528\u3044\u3066 \\(Tol \\space (\u8981\u6c42\u7cbe\u5ea6) = 10^{-6}, 10^{-7}, \\dots, 10^{-15}\\) \u3068\u5909\u5316\u3055\u305b\u3066\u8a08\u7b97\u3057\u305f. \u6bd4\u8f03\u306e\u305f\u3081\u30aa\u30a4\u30e9\u30fc\u6cd5 (Euler) \u3068 4 \u6b21\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5 (RK4) \u3082\u8868\u793a\u3057\u305f. \u3053\u3061\u3089\u306f \\(h = 0.01, \\space 0.005, \\space \\dots, \\space 10^{-5}\\) \u3068\u5909\u5316\u3055\u305b\u3066\u8a08\u7b97\u3057\u305f.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_5_exp2_3.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5735\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_5_exp2_3.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_5_exp2_3-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>x \u8ef8\u306f t = 16 \u306b\u304a\u3051\u308b \\(y_1, \\space y_2, \\space y_3\\) \u306e\u76f8\u5bfe\u8aa4\u5dee\u306e\u5e73\u5747\u3067, \u53f3\u306b\u3044\u304f\u307b\u3069\u5c0f\u3055\u3044 (\u7cbe\u5ea6\u304c\u3088\u3044).\u3000y \u8ef8\u306f\u305d\u306e\u3068\u304d\u306e\u95a2\u6570\u8a55\u4fa1\u56de\u6570\u3067\u3042\u308b. \u4e21\u8ef8\u3068\u3082\u5bfe\u6570\u76ee\u76db\u3067\u30d7\u30ed\u30c3\u30c8\u3057\u305f.<\/p>\n<p>\u3053\u306e\u554f\u984c\u306f\u7cbe\u5ea6\u304c\u51fa\u306b\u304f\u304f, t \u304c\u5927\u304d\u3044\u9818\u57df (\u4f8b\u3048\u3070, t = 50) \u3067\u306f\u9ad8\u7cbe\u5ea6\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u3067\u3082\u8a08\u7b97\u304c\u96e3\u3057\u3044\u3068\u3055\u308c\u308b (\u6587\u732e[5]). \u672c\u4f8b (t = 16) \u3067\u3082\u6700\u5927\u3067\u3082 \\(10^{-7} \\sim 10^{-8}\\) \u7a0b\u5ea6\u306e\u7cbe\u5ea6\u3057\u304b\u5f97\u3089\u308c\u306a\u3044. \u30aa\u30a4\u30e9\u30fc\u6cd5\u3067\u306f\u30b9\u30c6\u30c3\u30d7\u5e45\u3092\u5c0f\u3055\u304f\u3057\u3066\u3082\u610f\u5473\u306e\u3042\u308b\u5024\u306f\u5f97\u3089\u308c\u306a\u304b\u3063\u305f.<\/p>\n<h4>(3) \u30a2\u30ec\u30f3\u30b9\u30c8\u30fc\u30d5\u8ecc\u9053<\/h4>\n<p>\u5236\u9650\u4e09\u4f53\u554f\u984c\u306e\u4f8b\u3067\u3042\u308b. \u8cea\u91cf\u304c \\(\\mu\\) \u3068 \\(\\mu&#8217; (= 1 &#8211; \\mu)\\) \u306e 2 \u3064\u306e\u5929\u4f53 (\u6708\u3068\u5730\u7403\u3092\u60f3\u5b9a) \u304c\u5e73\u9762\u5185\u56de\u8ee2\u904b\u52d5\u3092\u3057\u3066\u304a\u308a, \u305d\u306e 2 \u3064\u306b\u6bd4\u3079\u3066\u8cea\u91cf\u304c\u7121\u8996\u3067\u304d\u308b\u7b2c 3 \u306e\u7269\u4f53\u304c\u540c\u4e00\u5e73\u9762\u5185\u3092\u904b\u52d5\u3059\u308b\u3082\u306e\u3068\u3059\u308b. \u6708\u3068\u5730\u7403\u306e\u5ea7\u6a19\u304c\u305d\u308c\u305e\u308c (1, 0) \u3068 (0, 0) \u306b\u56fa\u5b9a\u3055\u308c\u3066\u3044\u308b\u3088\u3046\u306a\u5ea7\u6a19\u7cfb\u3067\u8868\u3059\u3082\u306e\u3068\u3059\u308b. \u7b2c 3 \u306e\u7269\u4f53\u306e x \u5ea7\u6a19\u3092 \\(y_1\\), y \u5ea7\u6a19\u3092 \\(y_2\\) \u3067\u8868\u3059\u3068\u65b9\u7a0b\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&#038; y_1^{\\prime\\prime} = y_1 + 2y_2&#8242; &#8211; \\mu'(y_1 + \\mu)\/D_1 &#8211; \\mu(y_1 &#8211; \\mu&#8217;)\/D_2 \\\\<br \/>\n&#038; y_2^{\\prime\\prime} = y_2 &#8211; 2y_1&#8242; &#8211; \\mu&#8217;y_2\/D_1 &#8211; \\mu y_2\/D_2 \\\\<br \/>\n&#038; D_1 = ((y_1 + \\mu)^2 + y_2^2)^{3\/2} \\\\<br \/>\n&#038; D_2 = ((y_1 &#8211; \\mu&#8217;)^2 + y_2^2)^{3\/2} \\\\<br \/>\n&#038; \\mu = 0.012277471, \\mu&#8217; = 1 &#8211; \\mu \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\u6b21\u306e\u521d\u671f\u5024\u3092\u7528\u3044\u308b\u3068, t = 17.0652165601579625588917206249 \u3067\u5468\u671f\u89e3\u306b\u306a\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&#038; y_1(0) = 0.994, \\space y_1&#8242;(0) = 0 \\\\<br \/>\n&#038; y_2(0) = 0, \\space y_2&#8242;(0) = -2.00158510637908252240537862224 \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\u3053\u308c\u306f\u30a2\u30ec\u30f3\u30b9\u30c8\u30fc\u30d5\u8ecc\u9053\u3068\u3088\u3070\u308c\u3066\u304a\u308a, \u6b21\u306e\u3088\u3046\u306a\u8ecc\u9053\u306b\u306a\u308b.<\/p>\n<p><video width=\"640\" height=\"480\" controls><source src=\"\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_8_exp3_2.mp4\" type=\"video\/mp4\">Your browser does not support the video tag.<\/video><\/p>\n<p>\u7dd1\u306e\u4e38\u306f\u5730\u7403, \u8d64\u306e\u4e38\u306f\u6708, \u9752\u306e\u4e38\u306f\u7b2c 3 \u306e\u7269\u4f53\u3092\u8868\u3059.<\/p>\n<p>\u3053\u306e\u65b9\u7a0b\u5f0f\u306f 2 \u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306a\u306e\u3067 1 \u968e\u306e 4 \u5143\u9023\u7acb\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306b\u5909\u6570\u5909\u63db\u3057\u3066\u89e3\u304f. \u4e0a\u3068\u540c\u69d8\u306b, Derkfa, Dopri5a, Dverka, Dop853a, Deabm \u304a\u3088\u3073 Odexa \u3092\u7528\u3044\u3066 \\(Tol \\space (\u8981\u6c42\u7cbe\u5ea6) = 10^{-6}, 10^{-7}, \\dots, 10^{-15}\\) \u3068\u5909\u5316\u3055\u305b\u3066\u8a08\u7b97\u3057\u305f. \u6bd4\u8f03\u306e\u305f\u3081\u30aa\u30a4\u30e9\u30fc\u6cd5 (Euler) \u3068 4 \u6b21\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5 (RK4) \u3082\u8868\u793a\u3057\u305f. \u3053\u3061\u3089\u306f \\(h = 0.01, \\space 0.005, \\space \\dots, \\space 10^{-5}\\) \u3068\u5909\u5316\u3055\u305b\u3066\u8a08\u7b97\u3057\u305f.<\/p>\n<p>x \u8ef8\u306f 1 \u5468\u671f\u5f8c (t = 17.065216560158) \u306b\u304a\u3051\u308b \\(y_1, \\space y_2\\) \u306e\u76f8\u5bfe\u8aa4\u5dee\u306e\u5e73\u5747\u3067, \u53f3\u306b\u3044\u304f\u307b\u3069\u5c0f\u3055\u3044 (\u7cbe\u5ea6\u304c\u3088\u3044).\u3000y \u8ef8\u306f\u305d\u306e\u3068\u304d\u306e\u95a2\u6570\u8a55\u4fa1\u56de\u6570\u3067\u3042\u308b. \u4e21\u8ef8\u3068\u3082\u5bfe\u6570\u76ee\u76db\u3067\u30d7\u30ed\u30c3\u30c8\u3057\u305f.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_7_exp3_1.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5737\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_7_exp3_1.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_7_exp3_1-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>4 \u6b21\u306e\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5\u306e\u7d50\u679c\u3092\u898b\u308b\u3068\u672c\u6765 Derkfa (RKF45) \u3088\u308a\u5c11\u3057\u60aa\u3044\u7a0b\u5ea6\u306e\u306f\u305a\u3060\u304c\u306f\u308b\u304b\u306b\u591a\u304f\u306e\u95a2\u6570\u8a55\u4fa1\u56de\u6570\u3092\u5fc5\u8981\u3068\u3057\u3066\u3044\u308b. \u3053\u308c\u306f, \u95a2\u6570\u306e\u5024\u306e\u5909\u5316\u304c\u6025\u6fc0\u306a\u3068\u3053\u308d\u3068\u7de9\u3084\u304b\u306a\u3068\u3053\u308d\u306e\u5dee\u304c\u5927\u304d\u3044\u305f\u3081\u3068\u8003\u3048\u3089\u308c\u308b. \u3053\u306e\u3088\u3046\u306a\u554f\u984c\u3067\u306f\u30b9\u30c6\u30c3\u30d7\u5e45\u306e\u81ea\u52d5\u8abf\u7bc0\u6a5f\u80fd\u306e\u52b9\u679c\u304c\u5927\u304d\u3044\u3053\u3068\u304c\u308f\u304b\u308b.<\/p>\n<h4>(4) \u30a2\u30ec\u30f3\u30b9\u30c8\u30fc\u30d5\u8ecc\u9053 (2)<\/h4>\n<p>\u540c\u3058\u5236\u9650\u4e09\u4f53\u554f\u984c\u306e\u65b9\u7a0b\u5f0f\u3092\u7d76\u5bfe\u5ea7\u6a19\u7cfb\u3067\u8868\u3059\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&#038; y_1^{\\prime\\prime} = \\mu'(a_1(x) &#8211; y_1)\/D_1 + \\mu(b_1(x) &#8211; y_1)\/D_2 \\\\<br \/>\n&#038; y_2^{\\prime\\prime} = \\mu'(a_2(x) &#8211; y_2)\/D_1 + \\mu(b_2(x) &#8211; y_2)\/D_2 \\\\<br \/>\n&#038; D_1 = ((y_1 &#8211; a_1(x))^2 + (y_2 &#8211; a_2(x))^2)^{3\/2} \\\\<br \/>\n&#038; D_2 = ((y_1 &#8211; b_1(x))^2 + (y_2 &#8211; b_2(x))^2)^{3\/2} \\\\<br \/>\n&#038; a_1(x) = -\\mu cos(x), \\space a_2(x) = -\\mu sin(x) \\\\<br \/>\n&#038; b_1(x) = \\mu&#8217;cos(x), \\space b_2(x) = \\mu&#8217;sin(x) \\\\<br \/>\n&#038; \\mu = 0.012277471, \\space \\mu&#8217; = 1 &#8211; \\mu \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\u521d\u671f\u5024\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&#038; y_1(0) = 0.994, \\space y_1&#8242;(0) = 0 \\\\<br \/>\n&#038; y_2(0) = 0, \\space y_2&#8242;(0) = -2.00158510637908252240537862224 + 0.994 \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\u3053\u306e\u5ea7\u6a19\u7cfb\u3067\u306f 3 \u3064\u5168\u90e8\u306e\u5929\u4f53\u304c\u52d5\u304d, \u8ecc\u9053\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\n<p><video width=\"640\" height=\"480\" controls><source src=\"\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_11_exp4_2.mp4\" type=\"video\/mp4\">Your browser does not support the video tag.<\/video><\/p>\n<p>\u7dd1\u306e\u4e38\u306f\u5730\u7403, \u8d64\u306e\u4e38\u306f\u6708, \u9752\u306e\u4e38\u306f\u7b2c 3 \u306e\u7269\u4f53\u3092\u8868\u3059. \u308f\u305a\u304b\u3067\u306f\u3042\u308b\u304c\u5730\u7403\u3082\u52d5\u3044\u3066\u3044\u308b.<\/p>\n<p>\u3053\u306e\u65b9\u7a0b\u5f0f\u306f \\(y{\\prime\\prime} = f(t, y)\\) \u306e\u5f62\u306e 2 \u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306a\u306e\u3067, 1 \u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306b\u5909\u63db\u305b\u305a\u306b\u3053\u306e\u307e\u307e\u306e\u5f62\u3067\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u3053\u306e\u5f62\u5c02\u7528\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u4f7f\u3046\u3053\u3068\u304c\u3067\u304d\u308b.<\/p>\n<p>Dopn43, Dopn64, Dopn86, Dopn1210 \u304a\u3088\u3073 Odex2a \u3092\u7528\u3044\u3066 \\(Tol \\space (\u8981\u6c42\u7cbe\u5ea6) = 10^{-6}, 10^{-7}, \\dots, 10^{-15}\\) \u3068\u5909\u5316\u3055\u305b\u3066\u8a08\u7b97\u3057\u305f. \u6bd4\u8f03\u306e\u305f\u3081\u306b 4 \u6b21\u306e\u30cb\u30e5\u30b9\u30c8\u30ec\u30e0\u6cd5 (NY4) \u304a\u3088\u3073 5 \u6b21\u306e\u30cb\u30e5\u30b9\u30c8\u30ec\u30e0\u6cd5 (NY5) \u3082\u8868\u793a\u3057\u305f. \u3053\u3061\u3089\u306f \\(h = 0.01, \\space 0.005, \\space \\dots, \\space 10^{-5}\\) \u3068\u5909\u5316\u3055\u305b\u3066\u8a08\u7b97\u3057\u305f.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_10_exp4_1.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5743\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_10_exp4_1.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_10_exp4_1-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>(3) \u306e Derkfa \u3068 RK4 \u306e\u95a2\u4fc2\u3068\u540c\u69d8\u306b, Dopn43 \u306f NY4 \u304a\u3088\u3073 NY5 \u3068\u540c\u7a0b\u5ea6\u306e\u6027\u80fd\u304c\u4e88\u60f3\u3055\u308c\u305f\u304c\u5b9f\u969b\u306b\u306f\u304b\u306a\u308a\u5c11\u306a\u3044\u95a2\u6570\u8a55\u4fa1\u56de\u6570\u3067\u89e3\u3092\u6c42\u3081\u3066\u3044\u308b. \u3084\u306f\u308a, \u30b9\u30c6\u30c3\u30d7\u5e45\u306e\u81ea\u52d5\u8abf\u7bc0\u6a5f\u80fd\u306e\u52b9\u679c\u3067\u3042\u308b\u3068\u601d\u308f\u308c\u308b.<\/p>\n<h4>(5) \u5929\u6587\u529b\u5b66\u306e\u554f\u984c<\/h4>\n<p>\u5ea7\u6a19\u3068\u8cea\u91cf\u304c\u305d\u308c\u305e\u308c \\((x_i, y_i), \\space m_i = i \\space (i = 1, \\dots, 7)\\) \u306e 7 \u500b\u306e\u661f\u306e\u5e73\u9762\u5185\u306e\u904b\u52d5\u3067\u3042\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&#038; x_i^{\\prime\\prime} = \\sum_{j \\ne i} m_j(x_j) &#8211; x_i)\/r_{ij} \\\\<br \/>\n&#038; y_i^{\\prime\\prime} = \\sum_{j \\ne i} m_j(y_j) &#8211; y_i)\/r_{ij} \\\\<br \/>\n&#038; r_{ij} = ((x_j) &#8211; x_i)^2 + (y_j) &#8211; y_i)^2)^{3\/2} \\space (i, j = 1, \\dots, 7) \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\u521d\u671f\u5024\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3042\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&#038; x_1(0) = 3, x_2(0) = 3, x_3(0) = -1, x_4(0) = -3, x_5(0) = 2, x_6(0) = -2, x_7(0) = 2, \\\\<br \/>\n&#038; y_1(0) = 3, y_2(0) = -3, y_3(0) = 2, y_4(0) = 0, y_5(0) = 0, y_6(0) = -4, y_7(0) = 4, \\\\<br \/>\n&#038; x_6&#8242;(0) = 1.75, x_7&#8242;(0) = -1.5, x_i'(0) = = 0 \\space (\u305d\u306e\u4ed6\u306e i) \\\\<br \/>\n&#038; y_4&#8242;(0) = -1.25, y_5&#8242;(0) = 1, y_i'(0) = 0 \\space (\u305d\u306e\u4ed6\u306e i) \\\\<br \/>\n\\end{align}<br \/>\n\\]\nt = 0 \uff5e 3 \u3092\u8868\u793a\u3059\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\n<p><video width=\"640\" height=\"480\" controls><source src=\"\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_15_exp5_3.mp4\" type=\"video\/mp4\">Your browser does not support the video tag.<\/video><\/p>\n<p>\u3053\u306e\u533a\u9593\u3067\u306f 6 \u56de\u306e\u885d\u7a81\u304c\u8d77\u3053\u3063\u3066\u304a\u308a, \u305d\u306e\u3068\u304d\u306b\u8ecc\u9053\u3068\u52a0\u901f\u5ea6\u304c\u6025\u6fc0\u306b\u5909\u5316\u3059\u308b.<\/p>\n<p>\u3053\u306e\u65b9\u7a0b\u5f0f\u306f 7 \u5143\u306e 2 \u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306a\u306e\u3067 1 \u968e\u306e 14 \u5143\u9023\u7acb\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306b\u5909\u6570\u5909\u63db\u3057\u3066\u89e3\u304f. \u4e0a\u3068\u540c\u69d8\u306b, Derkfa, Dopri5a, Dverka, Dop853a, Deabm \u304a\u3088\u3073 Odexa \u3092\u7528\u3044\u3066 \\(Tol \\space (\u8981\u6c42\u7cbe\u5ea6) = 10^{-6}, 10^{-7}, \\dots, 10^{-15}\\) \u3068\u5909\u5316\u3055\u305b\u3066\u8a08\u7b97\u3057\u305f. \u6bd4\u8f03\u306e\u305f\u3081\u30aa\u30a4\u30e9\u30fc\u6cd5 (Euler) \u3068 4 \u6b21\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5 (RK4) \u3082\u8868\u793a\u3057\u305f. \u3053\u3061\u3089\u306f \\(h = 0.01, \\space 0.005, \\space \\dots, \\space 10^{-5}\\) \u3068\u5909\u5316\u3055\u305b\u3066\u8a08\u7b97\u3057\u305f.<\/p>\n<p>x \u8ef8\u306f t = 3 \u306b\u304a\u3051\u308b 7 \u3064\u306e\u5ea7\u6a19\u306e\u76f8\u5bfe\u8aa4\u5dee\u306e\u5e73\u5747\u3067, \u53f3\u306b\u3044\u304f\u307b\u3069\u5c0f\u3055\u3044 (\u7cbe\u5ea6\u304c\u3088\u3044).\u3000y \u8ef8\u306f\u305d\u306e\u3068\u304d\u306e\u95a2\u6570\u8a55\u4fa1\u56de\u6570\u3067\u3042\u308b. \u4e21\u8ef8\u3068\u3082\u5bfe\u6570\u76ee\u76db\u3067\u30d7\u30ed\u30c3\u30c8\u3057\u305f.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_13_exp5_1.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5752\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_13_exp5_1.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_13_exp5_1-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>RK4 \u306e\u7d50\u679c\u3092\u898b\u308b\u3068 (3) \u3068\u540c\u69d8\u306b\u30b9\u30c6\u30c3\u30d7\u5e45\u306e\u81ea\u52d5\u8abf\u7bc0\u6a5f\u80fd\u306e\u52b9\u679c\u304c\u5927\u304d\u3044\u3053\u3068\u304c\u308f\u304b\u308b.<\/p>\n<p>\u3088\u304f\u898b\u308b\u3068\u3053\u306e\u65b9\u7a0b\u5f0f\u306f \\(y^{\\prime\\prime} = f(t, y)\\) \u306e\u5f62\u306e 2 \u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306a\u306e\u3067, \u3053\u306e\u5f62\u5c02\u7528\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u4f7f\u3046\u3053\u3068\u304c\u3067\u304d\u3066, 7 \u5143\u306e 2 \u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u307e\u307e\u5909\u6570\u5909\u63db\u306a\u3057\u3067\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b. <\/p>\n<p>Dopn43, Dopn64, Dopn86, Dopn1210 \u304a\u3088\u3073 Odex2a \u3092\u7528\u3044\u3066 \\(Tol \\space (\u8981\u6c42\u7cbe\u5ea6) = 10^{-6}, 10^{-7}, \\dots, 10^{-15}\\) \u3068\u5909\u5316\u3055\u305b\u3066\u8a08\u7b97\u3059\u308b. \u6bd4\u8f03\u306e\u305f\u3081\u306b 4 \u6b21\u306e\u30cb\u30e5\u30b9\u30c8\u30ec\u30e0\u6cd5 (NY4) \u304a\u3088\u3073 5 \u6b21\u306e\u30cb\u30e5\u30b9\u30c8\u30ec\u30e0\u6cd5 (NY5) \u3082\u8868\u793a\u3057\u305f. \u3053\u3061\u3089\u306f \\(h = 0.01, \\space 0.005, \\space \\dots, \\space 10^{-5}\\) \u3068\u5909\u5316\u3055\u305b\u3066\u8a08\u7b97\u3057\u305f.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_14_exp5_2.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5753\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_14_exp5_2.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_14_exp5_2-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>\u3053\u3053\u3067\u3082\u30b9\u30c6\u30c3\u30d7\u5e45\u306e\u81ea\u52d5\u8abf\u7bc0\u6a5f\u80fd\u304c\u306a\u3044 NY4 \u304a\u3088\u3073 NY5 \u306f\u591a\u304f\u306e\u95a2\u6570\u8a08\u7b97\u3092\u5fc5\u8981\u3068\u3057\u3066\u304a\u308a, \u81ea\u52d5\u8abf\u7bc0\u6a5f\u80fd\u306e\u52b9\u679c\u304c\u308f\u304b\u308b.<\/p>\n<h4>(6) \u611f\u67d3\u30e2\u30c7\u30eb (\u9045\u5ef6\u5fae\u5206\u65b9\u7a0b\u5f0f)<\/h4>\n<p>\u9045\u5ef6\u5fae\u5206\u65b9\u7a0b\u5f0f (DDE) \u306e\u4f8b\u3068\u3057\u3066\u4f1d\u67d3\u6027\u75be\u60a3\u306e\u53e4\u5178\u7684\u30e2\u30c7\u30eb\u3092\u793a\u3059.<\/p>\n<p>\u4eba\u53e3\u306e\u4e2d\u3067 \\(y_1(t)\\) \u306f\u611f\u67d3\u53ef\u80fd\u306a\u4eba (susceptible), \\(y_2(t)\\) \u306f\u611f\u67d3\u8005 (infected), \\(y_3(t)\\) \u306f\u6cbb\u7652\u8005\u306a\u3069\u514d\u75ab\u304c\u3042\u308a\u611f\u67d3\u4e0d\u53ef\u80fd\u306a\u4eba (removed) \u306e\u6570\u3092\u793a\u3059\u5024\u3068\u3059\u308b. \u5358\u4f4d\u6642\u9593\u3042\u305f\u308a\u306b\u611f\u67d3\u3059\u308b\u4eba\u306e\u6570\u306f\u7a4d \\(y_1(t)y_2(t)\\) \u306b\u6bd4\u4f8b\u3057, \u65b0\u3057\u304f\u6cbb\u7652\u3057\u305f\u4eba\u306e\u6570\u306f\u611f\u67d3\u8005\u306e\u6570\u306b\u6bd4\u4f8b\u3059\u308b\u3068\u3059\u308c\u3070\u6b21\u306e\u30e2\u30c7\u30eb\u304c\u5f97\u3089\u308c\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&#038; y_1&#8242;(t) = -y_1(t)y_2(t) \\\\<br \/>\n&#038; y_2&#8242;(t) = y_1(t)y_2(t) &#8211;  y_2(t) \\\\<br \/>\n&#038; y_3&#8242;(t) = y_2(t) \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\u521d\u671f\u5024\u306f\u6b21\u306e\u3068\u304a\u308a\u3068\u3059\u308b.<br \/>\n\\[<br \/>\ny_1(0) = 5, \\space y_2(0) = 0.1, \\space y_3(0) = 1<br \/>\n\\]\n\u3053\u306e\u30e2\u30c7\u30eb\u3067\u306f\u6b21\u306e\u3088\u3046\u306b\u5168\u54e1\u304c\u611f\u67d3\u3057\u3066\u305d\u3057\u3066\u6cbb\u7652\u3057\u3066\u514d\u75ab\u3092\u7372\u5f97\u3059\u308b\u306e\u3067\u305d\u308c\u4ee5\u4e0a\u4f55\u3082\u8d77\u3053\u3089\u306a\u304f\u306a\u308b.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_16_exp6.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5758\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_16_exp6.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_16_exp6-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>\u3082\u3057\u514d\u75ab\u3092\u6301\u3064\u4eba\u304c\u4e00\u5b9a\u671f\u9593 \\(\\tau\\) \u5f8c\u306b\u514d\u75ab\u306e\u52b9\u679c\u304c\u306a\u304f\u306a\u308a\u518d\u3073\u611f\u67d3\u53ef\u80fd\u306b\u306a\u308b\u3068\u3059\u308b\u3068\u5468\u671f\u7684\u306b\u611f\u67d3\u75c7\u304c\u767a\u751f\u3059\u308b\u3068\u4e88\u60f3\u3055\u308c\u308b. \u307e\u305f, \u6f5c\u4f0f\u671f\u9593 \\(\\tau_2\\) \u3082\u5c0e\u5165\u3059\u308b\u3053\u3068\u306b\u3059\u308c\u3070\u6b21\u306e\u30e2\u30c7\u30eb\u304c\u5f97\u3089\u308c, \u904e\u53bb\u306e\u5024\u304c\u5fc5\u8981\u306a\u9045\u5ef6\u5fae\u5206\u65b9\u7a0b\u5f0f\u3068\u306a\u308a\u901a\u5e38\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u3067\u306f\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u306a\u3044.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&#038; y_1&#8242;(t) = -y_1(t)y_2(t &#8211; \\tau_2) + y_2(t &#8211; \\tau) \\\\<br \/>\n&#038; y_2&#8242;(t) = y_1(t)y_2(t &#8211; \\tau_2) &#8211;  y_2(t) \\\\<br \/>\n&#038; y_3&#8242;(t) = y_2(t) &#8211; y_2(t &#8211; \\tau) \\\\<br \/>\n\\end{align}<br \/>\n\\]\nXLPack \u306e Retarda \u306f\u30c9\u30eb\u30de\u30f3\u30fb\u30d7\u30ea\u30f3\u30b9\u6cd5\u30d7\u30ed\u30b0\u30e9\u30e0 Dopri5a \u3092\u9045\u5ef6\u5fae\u5206\u65b9\u7a0b\u5f0f\u7528\u306b\u4fee\u6b63\u3057\u305f\u3082\u306e\u3067\u3042\u308b. Dopri5a \u3067\u306f\u5bc6\u51fa\u529b\u306e\u305f\u3081\u306b 1 \u30b9\u30c6\u30c3\u30d7\u524d\u307e\u3067\u306e\u904e\u53bb\u306e\u5024\u3092\u4fdd\u6301\u3059\u308b\u304c, Retarda \u306f\u305a\u3063\u3068\u524d\u307e\u3067\u306e\u5024\u3092\u4fdd\u6301\u3059\u308b\u3088\u3046\u306b\u306a\u3063\u3066\u3044\u308b.<\/p>\n<p>\\(\\tau = 10, \\space \\tau_2 = 1\\) \u3068\u3057\u3066 Retarda \u3092\u4f7f\u3063\u3066\u8a08\u7b97\u3059\u308b\u3068, \u6b21\u306e\u3088\u3046\u306b\u5468\u671f\u7684\u767a\u751f\u306e\u56f3\u304c\u5f97\u3089\u308c\u305f. \u521d\u671f\u5024\u306f\u4e0a\u3068\u540c\u3058\u3067\u3042\u308b\u304c, \u9045\u5ef6\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u5b9a\u7fa9\u3067\u306f \\(t = -\\tau \\sim 0\\) \u306e\u5024\u3082\u5fc5\u8981\u306b\u306a\u308b. \u3053\u3053\u3067\u306f\u521d\u671f\u5024\u3068\u540c\u3058\u5024\u3092\u3068\u308b\u3082\u306e\u3068\u3057\u305f.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_17_exp6_1.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5759\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_17_exp6_1.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_17_exp6_1-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<h3>10.4.3 \u30b9\u30c6\u30a3\u30d5\u306a\u554f\u984c<\/h3>\n<p>\u672c\u7bc0\u306e\u4f8b\u984c\u306e\u8a73\u7d30\u306f\u53c2\u8003\u6587\u732e[6]\u3092\u53c2\u7167\u306e\u3053\u3068.<\/p>\n<p>Debdf (BDF), Seulexa (\u88dc\u5916\u6cd5) \u304a\u3088\u3073 Radaua (5 \u6b21 \uff5e 13 \u6b21\u53ef\u5909 IRK) \u306f\u554f\u984c\u306b\u3088\u308b\u304c, \u540c\u7a0b\u5ea6\u306e\u7d50\u679c\u3067\u3042\u3063\u305f. Rodasa (\u30ed\u30fc\u30bc\u30f3\u30d6\u30ed\u30c3\u30af\u6cd5) \u306f\u307b\u304b\u306b\u6bd4\u3079\u3066\u9045\u3044\u3088\u3046\u306b\u307f\u3048\u308b\u304c, \u3053\u3053\u3067\u306f\u95a2\u6570\u8a55\u4fa1\u56de\u6570\u3067\u3057\u304b\u8a55\u4fa1\u3057\u3066\u3044\u306a\u3044\u305f\u3081\u3067\u3042\u308a\u7dcf\u8a08\u7b97\u91cf\u306f\u591a\u304f\u306a\u3044\u53ef\u80fd\u6027\u304c\u3042\u308b.<\/p>\n<h4>(1) \u30d5\u30a1\u30f3\u30fb\u30c7\u30eb\u30fb\u30dd\u30eb\u632f\u52d5\u5b50<\/h4>\n<p>\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f<br \/>\n\\[<br \/>\ny^{\\prime\\prime} + \\alpha y&#8217; + y = 0<br \/>\n\\]\n\u306e\u89e3\u306f, \\(\\alpha > 0\\) \u306a\u3089\u3070\u6e1b\u8870\u3057, \\(\\alpha < 0\\) \u306a\u3089\u3070\u4e0d\u5b89\u5b9a\u306b\u306a\u308b.\n\ny \u304c\u5c0f\u3055\u3044\u3068\u304d\u306f \\(\\alpha > 0\\) \u306b, y \u304c\u5927\u304d\u3044\u3068\u304d\u306f \\(\\alpha < 0\\) \u3068\u306a\u308b\u3088\u3046\u306b \\(\\alpha\\) \u3092\u5909\u5316\u3055\u305b\u308b\u305f\u3081\u306b \\(\\alpha = \\epsilon(y^2 - 1) \\space (\\epsilon > 0)\\) \u3068\u3057, \u3055\u3089\u306b \\(y_1&#8242; = y_2\\) \u3068\u304a\u304f\u3068\u6b21\u306e\u9023\u7acb\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u304c\u5f97\u3089\u308c\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&#038; y_1&#8242; = y_2 \\\\<br \/>\n&#038; y_2&#8242; = \\epsilon(1 &#8211; y_1^2)y_2 &#8211; y_1 \\space (\\epsilon > 0) \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\u3053\u306e\u65b9\u7a0b\u5f0f\u3067\u306f, \u5c0f\u3055\u3044\u632f\u52d5\u306f\u5897\u5e45\u3055\u308c, \u5927\u304d\u3044\u632f\u52d5\u306f\u6e1b\u8870\u3055\u308c\u308b. \u305d\u306e\u305f\u3081, \u3059\u3079\u3066\u306e\u89e3\u304c\u305d\u3053\u3078\u53ce\u675f\u3059\u308b\u3088\u3046\u306a\u5b89\u5b9a\u306a\u5468\u671f\u89e3 (\u6975\u9650\u5468\u671f\u8ecc\u9053) \u304c\u5b58\u5728\u3059\u308b. \\(\\epsilon = 1\\), \u521d\u671f\u5024 \\(y_1(0) = 2, y_2(0) = -2\\) \u3092\u59cb\u70b9\u3068\u3057\u305f\u5834\u5408, \u6b21\u306e\u3088\u3046\u306b\u5468\u671f\u8ecc\u9053\u306b\u5165\u308b.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_18_exp7.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5762\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_18_exp7.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_18_exp7-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>Debdf, Radaua (\u6b21\u6570\u81ea\u52d5\u53ef\u5909), Rodasa \u304a\u3088\u3073 Seulexa \u306e\u6bd4\u8f03\u3092\u884c\u3046. \u3053\u3053\u3067\u306f, \\(\\epsilon = 10^{-6}\\), \u521d\u671f\u5024 \\(y_1(0) = 2, y_2(0) = 0\\) \u3068\u3059\u308b. \\(Tol (\u8981\u6c42\u7cbe\u5ea6) = 10^{-6}, 10^{-7}, \\dots, 10^{-15}\\) \u3068\u5909\u5316\u3055\u305b\u3066\u8a08\u7b97\u3057\u305f\u3068\u304d\u306b\u5f97\u3089\u308c\u305f \\(t = 11\\) \u306b\u304a\u3051\u308b \\(y_1\\) \u304a\u3088\u3073 \\(y_2\\) \u306e\u76f8\u5bfe\u8aa4\u5dee\u306e\u5e73\u5747\u306b\u5bfe\u3059\u308b\u95a2\u6570\u8a55\u4fa1\u56de\u6570\u3092\u4e21\u5bfe\u6570\u30d7\u30ed\u30c3\u30c8\u3059\u308b. \u76f8\u5bfe\u8aa4\u5dee\u306e\u5e73\u5747\u306f\u53f3\u306b\u3044\u304f\u307b\u3068\u5c11\u306a\u3044 (\u7cbe\u5ea6\u304c\u3088\u3044).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_19_exp7_1.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5763\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_19_exp7_1.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_19_exp7_1-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<h4>(2) \u30aa\u30ec\u30b4\u30cd\u30fc\u30bf<\/h4>\n<p>3 \u6b21\u5143\u306e\u6975\u9650\u5468\u671f\u8ecc\u9053\u3092\u6301\u3064\u5316\u5b66\u53cd\u5fdc\u30e2\u30c7\u30eb\u3067, \u6b21\u306e\u5f0f\u3067\u8868\u3055\u308c\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&#038; y_1&#8242; = 77.27(y_2 + y_1(1 &#8211; 8.375\u00d710^{-6}y_1 &#8211; y_2)) \\\\<br \/>\n&#038; y_2&#8242; = (1\/77.27)(y_3 &#8211; (1 + y_1)y_2) \\\\<br \/>\n&#038; y_3&#8242; = 0.161(y_1 &#8211; y_3) \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\u521d\u671f\u5024\u306f \\(y_1(0) = 1, \\space y_2(0) = 2, \\space y_3(0) = 3\\) \u3067\u3042\u308b.<\/p>\n<p>\u6b21\u306e\u3088\u3046\u306b\u89e3\u306e\u7d76\u5bfe\u5024\u306e\u30aa\u30fc\u30c0\u30fc\u304c\u6025\u6fc0\u306b\u5909\u5316\u3059\u308b\u30b9\u30c6\u30a3\u30d5\u306a\u65b9\u7a0b\u5f0f\u3067\u3042\u308b.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_20_exp8.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5771\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_20_exp8.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_20_exp8-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>\u6975\u9650\u5468\u671f\u8ecc\u9053\u304c\u5b58\u5728\u3059\u308b.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_21_exp8_1.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5772\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_21_exp8_1.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_21_exp8_1-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>\u4e0a\u3068\u540c\u69d8\u306b, Debdf, Radaua (\u6b21\u6570\u81ea\u52d5\u53ef\u5909), Rodasa \u304a\u3088\u3073 Seulexa \u306e\u6bd4\u8f03\u3092\u884c\u3046. \\(Tol (\u8981\u6c42\u7cbe\u5ea6) = 10^{-6}, 10^{-7}, \\dots, 10^{-15}\\) \u3068\u5909\u5316\u3055\u305b\u3066\u8a08\u7b97\u3057\u305f\u3068\u304d\u306b\u5f97\u3089\u308c\u305f \\(t = 360\\) \u306b\u304a\u3051\u308b \\(y_1, \\space y_2\\) \u304a\u3088\u3073 \\(y_3\\) \u306e\u76f8\u5bfe\u8aa4\u5dee\u306e\u5e73\u5747\u306b\u5bfe\u3059\u308b\u95a2\u6570\u8a55\u4fa1\u56de\u6570\u3092\u4e21\u5bfe\u6570\u30d7\u30ed\u30c3\u30c8\u3059\u308b. \u76f8\u5bfe\u8aa4\u5dee\u306e\u5e73\u5747\u306f\u53f3\u306b\u3044\u304f\u307b\u3068\u5c11\u306a\u3044 (\u7cbe\u5ea6\u304c\u3088\u3044).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_22_exp8_2.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5773\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_22_exp8_2.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_22_exp8_2-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<h4>(3) \u30d6\u30e9\u30bb\u30ec\u30fc\u30bf<\/h4>\n<p>\u30d6\u30e9\u30bb\u30ec\u30fc\u30bf\u306f\u6b21\u306e\u53cd\u5fdc\u5f0f\u3067\u8868\u3055\u308c\u308b\u4eee\u60f3\u7684\u306a\u5316\u5b66\u53cd\u5fdc\u7cfb\u3067\u3042\u308b.<\/p>\n<pre>  \r\n            k<sub>1<\/sub>\r\n       A  -----&gt;  X\r\n            k<sub>2<\/sub>\r\n   B + X  -----&gt;  Y + D (2 \u5206\u5b50\u53cd\u5fdc)\r\n            k<sub>3<\/sub>\r\n  2X + Y  -----&gt;  3X    (\u81ea\u5df1\u89e6\u5a92 3 \u5206\u5b50\u53cd\u5fdc)\r\n            k<sub>4<\/sub>\r\n       X  -----&gt;  E\r\n\r\n<\/pre>\n<p>&nbsp;<br \/>\nA \u3068 B \u306f\u4e00\u5b9a\u5024\u3067\u3042\u308b\u3068\u3057, \u307e\u305f, \u53cd\u5fdc\u901f\u5ea6 \\(k_i\\) \u3092\u3059\u3079\u3066 1 \u306b\u3057\u3066 \\(u(t) = X(t), v(t) = Y(t)\\) \u3068\u304a\u3051\u3070\u6b21\u5f0f\u304c\u5f97\u3089\u308c\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&#038; u&#8217; = A + u^2v &#8211; (B + 1)u \\\\<br \/>\n&#038; v&#8217; = Bu &#8211; u^2v \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\u62e1\u6563\u3092\u4f34\u3046\u5834\u5408\u306b\u306f\u62e1\u6563\u9805\u3092\u8ffd\u52a0\u3057\u305f\u504f\u5fae\u5206\u65b9\u7a0b\u5f0f\u306b\u306a\u308b. 1 \u6b21\u5143\u306e\u5834\u5408\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&#038; \\frac{\\partial u}{\\partial t} = A + u^2v &#8211; (B + 1)u + \\alpha \\frac{\\partial^2u}{\\partial x^2} \\\\<br \/>\n&#038; \\frac{\\partial v}{\\partial t} = Bu &#8211; u^2v + \\alpha \\frac{\\partial^2v}{\\partial x^2} \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\u3053\u3053\u3067, \\(0 \\le x \\le 1, \\space A = 1, \\space B = 3, \\space \\alpha = 1\/50\\) \u3068\u3057, \u5883\u754c\u6761\u4ef6, \u521d\u671f\u6761\u4ef6\u3092\u6b21\u306e\u3088\u3046\u306b\u3059\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&#038; u(0, t) = u(1, t) = 1, \\space v(0, t) = v(1, t) = 3 \\\\<br \/>\n&#038; u(x, 0) = 1 + \\frac{1}{2}sin(2\\pi x), \\space v(x, 0) = 3 \\\\<br \/>\n\\end{align}<br \/>\n\\]\nx \u306b\u95a2\u3059\u308b 2 \u968e\u5fae\u5206\u3092 \\(x_1 = i\/(N + 1) \\space (1 \\le i \\le N), \\space \\Delta x = 1\/(N + 1)\\) \u306e N \u70b9\u683c\u5b50\u4e0a\u306e\u5dee\u5206\u3067\u7f6e\u304d\u63db\u3048\u308b\u3068\u6b21\u306e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u7cfb\u304c\u5f97\u3089\u308c\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&#038; u&#8217; = 1 + u_i^2v_i &#8211; 4u_i + \\frac{\\alpha}{(\\Delta x)^2}(u_{i-1} &#8211; 2u_i + u_{i+1}) \\\\<br \/>\n&#038; v&#8217; = 3u_i &#8211; u_i^2v_i + \\frac{\\alpha}{(\\Delta x)^2}(v_{i-1} &#8211; 2v_i + v_{i+1}) \\\\<br \/>\n&#038; u_0(t) = u_{N+1}(t) = 1, \\space v_0(t) = v_{N+1}(t) = 3 \\\\<br \/>\n&#038; u_i(0) = 1 + \\frac{1}{2}sin(2\\pi x_i), \\space v_i(0) = 3 \\space (i = 1, \\dots, N) \\\\<br \/>\n\\end{align}<br \/>\n\\]\nN = 500 \u3068\u3059\u308b\u3068, \u6700\u5927\u56fa\u6709\u5024\u7d04 -20000 \u3092\u6301\u3064\u30b9\u30c6\u30a3\u30d5\u306a 1000 \u5143\u306e\u5fae\u5206\u65b9\u7a0b\u5f0f\u7cfb\u306b\u306a\u308b. \u7aef\u4ed8\u8fd1 (x \u304c 0 \u307e\u305f\u306f 1 \u306b\u8fd1\u3044\u3068\u3053\u308d) \u3068\u4e2d\u592e\u4ed8\u8fd1 (x \u304c 0.5 \u4ed8\u8fd1)\u306e\u5024\u3092\u30d7\u30ed\u30c3\u30c8\u3059\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u3063\u305f.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_23_exp9.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5775\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_23_exp9.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_23_exp9-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>\u4e0a\u3068\u540c\u69d8\u306b, Debdf, Radaua (\u6b21\u6570\u81ea\u52d5\u53ef\u5909), Rodasa \u304a\u3088\u3073 Seulexa \u306e\u6bd4\u8f03\u3092\u884c\u3046. \\(Tol (\u8981\u6c42\u7cbe\u5ea6) = 10^{-6}, 10^{-7}, \\dots, 10^{-15}\\) \u3068\u5909\u5316\u3055\u305b\u3066\u8a08\u7b97\u3057\u305f\u3068\u304d\u306b\u5f97\u3089\u308c\u305f \\(t = 10\\) \u306b\u304a\u3051\u308b\u4e0a\u56f3\u306e 6 \u70b9\u306e\u5024\u306e\u76f8\u5bfe\u8aa4\u5dee\u306e\u5e73\u5747\u306b\u5bfe\u3059\u308b\u95a2\u6570\u8a55\u4fa1\u56de\u6570\u3092\u4e21\u5bfe\u6570\u30d7\u30ed\u30c3\u30c8\u3059\u308b. \u76f8\u5bfe\u8aa4\u5dee\u306e\u5e73\u5747\u306f\u53f3\u306b\u3044\u304f\u307b\u3068\u5c11\u306a\u3044 (\u7cbe\u5ea6\u304c\u3088\u3044).<\/p>\n<p>\u306a\u304a, \u3053\u306e\u554f\u984c\u306e\u5834\u5408, \u9023\u7acb\u65b9\u7a0b\u5f0f\u306e\u5143\u6570\u304c\u5927\u304d\u304f\u30e4\u30b3\u30d3\u884c\u5217\u304c\u4e0a\u4e0b 2 \u306e\u5e2f\u5e45\u306e\u5e2f\u884c\u5217\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u3063\u3066\u3044\u308b\u306e\u3067, Mljac = Mujac = 2 (Debdf \u306e\u5834\u5408\u306f Ml = Mu = 2) \u3068\u8a2d\u5b9a\u3057\u3066\u304a\u304f\u3053\u3068\u304c\u3067\u304d\u308b. \u305d\u3046\u3057\u306a\u3044\u3068\u8a08\u7b97\u91cf\u304c\u81a8\u5927\u306b\u306a\u3063\u3066\u3057\u307e\u3046.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_24_exp9_1.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5776\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_24_exp9_1.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_24_exp9_1-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<h3>10.4.4 \u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f<\/h3>\n<h4>(1) \u5358\u632f\u308a\u5b50<\/h4>\n<p>\u300c10.3.3.1 \u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f\u300d\u306b\u304a\u3044\u3066\u53d6\u308a\u4e0a\u3052\u305f\u5358\u632f\u308a\u5b50\u3092\u76f4\u4ea4\u5ea7\u6a19\u7cfb\u3067\u8868\u3057\u305f\u4f8b\u306b\u3064\u3044\u3066\u518d\u3073\u8003\u3048\u308b.<\/p>\n<p>\u4e0b\u56f3\u306e\u3088\u3046\u306b, \u9577\u3055 \\(l [m]\\) \u306e\u7cf8\u306b\u91cd\u3055 \\(m [kg]\\) \u306e\u304a\u3082\u308a\u304c\u3064\u3044\u305f\u632f\u308a\u5b50\u3092\u8003\u3048\u308b. \u304a\u3082\u308a\u306e\u4f4d\u7f6e\u306f \\((q_1, q_2)\\) \u3068\u3059\u308b. \\(g [m\/s^2]\\) \u306f\u91cd\u529b\u52a0\u901f\u5ea6\u3067\u3042\u308b.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2020\/06\/ode_pendulum_xy-300x225.png\" alt=\"\" width=\"300\" height=\"225\" class=\"aligncenter size-medium wp-image-2610\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2020\/06\/ode_pendulum_xy-300x225.png 300w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2020\/06\/ode_pendulum_xy.png 606w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>\u3053\u306e\u632f\u308a\u5b50\u306e\u904b\u52d5\u306f\u6b21\u306e\u5e38\u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f\u3067\u8868\u3055\u308c\u308b. \\(v_1, v_2\\) \u306f \\(q_1, q_2\\) \u65b9\u5411\u306e\u901f\u5ea6\u3067\u3042\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&#038; q_1&#8242; = v_1 \\\\<br \/>\n&#038; q_2&#8242; = v_2 \\\\<br \/>\n&#038; v_1&#8242; = -\\lambda q_1 \\\\<br \/>\n&#038; v_2&#8242; = -\\lambda q_2 &#8211; g \\\\<br \/>\n&#038; 0 = q_1^2 + q_2^2 &#8211; l^2 \\space [\u6307\u6570 3] \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\u3053\u306e\u5f0f\u306f\u6307\u6570 3 \u3067\u3042\u308b. \u6700\u5f8c\u306e\u5f0f\u3092\u3092\u5fae\u5206\u3057\u3066\u5f97\u3089\u308c\u308b\u6307\u6570 2 \u304a\u3088\u3073\u6307\u6570 1 \u306e\u5f0f\u306f\u6b21\u306e\u3088\u3046\u3067\u3042\u3063\u305f.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&#038; 0 = q_1v_1 + q_2v_2 \\space [\u6307\u6570 2] \\\\<br \/>\n&#038; 0 = -\\lambda &#8211; g q_2 + v_1^2 + v_2^2 \\space [\u6307\u6570 1] \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\u3055\u3089\u306b, \\(\\lambda\\) [\u6307\u6570 1] \u3092\u5143\u306e\u9023\u7acb\u65b9\u7a0b\u5f0f\u306b\u4ee3\u5165\u3059\u308b\u3068\u6b21\u306e 4 \u5143\u9023\u7acb\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (\u6307\u6570 0) \u304c\u5f97\u3089\u308c\u305f.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&#038; q_1&#8242; = v_1 \\\\<br \/>\n&#038; q_2&#8242; = v_2 \\\\<br \/>\n&#038; v_1&#8242; = (gq_2 &#8211; v_1^2 &#8211; v_2^2)q_1 \\\\<br \/>\n&#038; v_2&#8242; = (gq_2 &#8211; v_1^2 &#8211; v_2^2)q_2 &#8211; g \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\u4ee5\u4e0a\u306e\u5f0f\u3092\u4f7f\u3063\u3066 \\(t = 0 (q_1 = sin(\\pi\/4), q_2 = -cos(\\pi\/4), v_1 = 0, v_2 = 0)\\) \u304b\u3089\u59cb\u3081\u3066 2 \u5468\u671f\u5f8c\u306e\u4f4d\u7f6e\u3092\u6c42\u3081\u305d\u306e\u76f8\u5bfe\u8aa4\u5dee\u3068\u95a2\u6570\u8a08\u7b97\u56de\u6570 (\u4e0a\u306e 5 \u672c\u306e\u5f0f\u3092\u30bb\u30c3\u30c8\u3067\u8a08\u7b97\u3057\u3066 1 \u56de\u3068\u30ab\u30a6\u30f3\u30c8\u3059\u308b) \u3092\u30d7\u30ed\u30c3\u30c8\u3059\u308b. \u306a\u304a, \\(Tol = 10^{-4}, 10^{-5}, \\dots, 10^{-12}\\) \u3068\u5909\u3048\u3066\u8a08\u7b97\u3057\u305f.<\/p>\n<p>\u30d7\u30ed\u30b0\u30e9\u30e0\u306f Radaua, Rodasa \u304a\u3088\u3073 Seulexa \u3092\u4f7f\u7528\u3057\u305f. \u3053\u308c\u3089\u306f Mu&#8217; = \u03c6(u) \u578b\u306e\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u4f5c\u3089\u308c\u3066\u3044\u3066, \u8cea\u91cf\u30de\u30c8\u30ea\u30c3\u30af\u30b9 M \u304c\u5358\u4f4d\u884c\u5217\u306e\u5834\u5408 (M = I) \u306b\u306f\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u9670\u89e3\u6cd5\u3067\u89e3\u304d, \u305d\u3046\u3067\u306a\u3044\u5834\u5408\u306b\u306f\u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f (DAE) \u3092\u89e3\u304f. \u3053\u306e\u5834\u5408 M \u3092\u6b21\u306e\u3088\u3046\u306b\u8a2d\u5b9a\u3057\u305f.<br \/>\n\\[<br \/>\nM =<br \/>\n\\begin{pmatrix}<br \/>\n1 \\\\<br \/>\n &#038; 1 \\\\<br \/>\n &#038; &#038; 1 \\\\<br \/>\n &#038; &#038; &#038; 1 \\\\<br \/>\n &#038; &#038; &#038; &#038; 0 \\\\<br \/>\n\\end{pmatrix}<br \/>\n\\]\nRadaua \u306f\u6307\u6570 2 \u3068 3 \u306b\u9069\u7528\u3059\u308b\u3068\u304d\u306f\u30d1\u30e9\u30e1\u30fc\u30bf Nind1, Nind2, Nind3 \u3092\u8a2d\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a, \u3053\u3053\u3067\u306f\u305d\u308c\u305e\u308c 4, 0, 1 \u3068\u8a2d\u5b9a\u3057\u305f.<\/p>\n<p>\u3055\u3089\u306b, \u6bd4\u8f03\u306e\u305f\u3081\u306b 4 \u5143\u9023\u7acb\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (\u6307\u6570 0) \u3092 Derkfa \u3067\u89e3\u3044\u305f\u5834\u5408 (\u5b89\u5b9a\u5316\u306a\u3057) \u306e\u7d50\u679c\u3082\u30d7\u30ed\u30c3\u30c8\u3057\u305f.<\/p>\n<h4>(i) \u6307\u6570 1 \u306e\u5834\u5408<\/h4>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_25_exp10_1.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5797\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_25_exp10_1.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_25_exp10_1-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>Radaua \u306f\u6307\u6570 3 \u307e\u3067, Rodasa \u304a\u3088\u3073 Seulexa \u306f\u6307\u6570 1 \u306b\u9069\u7528\u3067\u304d\u308b\u304c, \u305d\u308c\u305e\u308c\u89e3\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u305f.<\/p>\n<h4>(ii) \u6307\u6570 2 \u306e\u5834\u5408<\/h4>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_26_exp10_2.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5798\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_26_exp10_2.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_26_exp10_2-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>Seulexa \u306f\u6307\u6570 2 \u306f\u9069\u7528\u7bc4\u56f2\u5916\u3067\u3042\u308b\u304c\u89e3\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u305f. \u305f\u3060\u3057, \u8a08\u7b97\u91cf\u306f\u591a\u304b\u3063\u305f. Rodasa \u306f\u4f4e\u7cbe\u5ea6\u306e\u9818\u57df\u3067\u306f\u89e3\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u305f\u304c\u8a08\u7b97\u91cf\u306f\u975e\u5e38\u306b\u591a\u304b\u3063\u305f.<\/p>\n<h4>(iii) \u6307\u6570 3 \u306e\u5834\u5408<\/h4>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_27_exp10_3.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5799\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_27_exp10_3.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_27_exp10_3-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>\u6307\u6570 3 \u3067\u4f7f\u3048\u308b\u306e\u306f Radaua \u3067\u3042\u308b\u304c, Derkfa (\u6307\u6570 0) \u306b\u6bd4\u3079\u308b\u3068\u8a08\u7b97\u91cf\u306f\u591a\u3044. \u307e\u305f, \u6b21\u6570 (5, 9, 13 \u6b21) \u3092\u81ea\u52d5\u9078\u629e\u3059\u308b\u3088\u3046\u306b\u3059\u308b\u3068\u4e0d\u5b89\u5b9a\u306b\u306a\u3063\u305f\u305f\u3081, \u3053\u3053\u3067\u306f 5 \u6b21\u306b\u56fa\u5b9a\u3057\u305f.<\/p>\n<p>\u3084\u306f\u308a\u6307\u6570 3 \u3067\u306f\u8a08\u7b97\u304c\u96e3\u3057\u304f\u306a\u308b\u3088\u3046\u3067\u3042\u308b. \u3067\u304d\u308b\u3060\u3051\u6307\u6570\u304c\u4f4e\u304f\u306a\u308b\u3088\u3046\u306b\u5b9a\u5f0f\u5316\u3057\u305f\u65b9\u304c\u3088\u3055\u305d\u3046\u3067\u3042\u308b.<\/p>\n<h4>(4) \u30c8\u30e9\u30f3\u30b8\u30b9\u30bf\u30fc\u56de\u8def<\/h4>\n<p>\u6b21\u306e\u30c8\u30e9\u30f3\u30b8\u30b9\u30bf\u30fc\u5897\u5e45\u56de\u8def\u3092\u8003\u3048\u308b. \u56f3\u306e\u4e2d\u3067 \\(1, 2, \\dots, 5\\) \u306e\u70b9\u306b\u304a\u3051\u308b\u96fb\u5727\u3092 \\(U_1, U_2, \\dots, U_5\\) \u3068\u3059\u308b. \\(U_e(t)\\) \u306f\u5165\u529b\u4fe1\u53f7\u96fb\u5727, \\(U_b\\) \u306f\u96fb\u6e90\u96fb\u5727\u3067\u3042\u308b (\\(U_b = 6 V\\)). \u51fa\u529b\u4fe1\u53f7\u306f 5 \u306b\u304a\u3051\u308b\u96fb\u5727 \\(U_5\\) \u3068\u3057\u3066\u53d6\u308a\u51fa\u3059\u3053\u3068\u304c\u3067\u304d\u308b.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2020\/06\/ode_tr_0.png\" alt=\"\" width=\"640\" height=\"400\" class=\"aligncenter size-full wp-image-2627\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2020\/06\/ode_tr_0.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2020\/06\/ode_tr_0-300x188.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>\u62b5\u6297 R \u3092\u6d41\u308c\u308b\u96fb\u6d41\u306f \\(I = U\/R\\), \u30b3\u30f3\u30c7\u30f3\u30b5 C \u3092\u6d41\u308c\u308b\u96fb\u6d41\u306f \\(I = C dU\/dt\\) \u3092\u6e80\u305f\u3059. \u30c8\u30e9\u30f3\u30b8\u30b9\u30bf\u3067\u306f 2 \u304b\u3089 3 \u306b\u6d41\u308c\u308b\u96fb\u6d41\u304c 99 \u500d\u5897\u5e45\u3055\u308c\u3066 4 \u304b\u3089 3 \u306b\u6d41\u308c\u308b\u96fb\u6d41\u306b\u306a\u308b\u3082\u306e\u3068\u3057, \u3053\u308c\u3089\u306e\u96fb\u6d41\u306f\u96fb\u4f4d\u5dee \\(U2 &#8211; U3\\) \u306b\u4f9d\u5b58\u3057, \u95a2\u6570 \\(f(U2 &#8211; U3)\\) \u3067\u8868\u3055\u308c\u3082\u306e\u3068\u3059\u308b. \u30ad\u30eb\u30d2\u30db\u30c3\u30d5\u306e\u6cd5\u5247\u306b\u3088\u308a\u3042\u308b\u70b9\u306b\u51fa\u5165\u308a\u3059\u308b\u96fb\u6d41\u306e\u548c\u306f\u30bc\u30ed\u3067\u3042\u308b\u304b\u3089, \u70b9 \\(1, 2, \\dots, 5\\) \u306b\u304a\u3044\u3066\u65b9\u7a0b\u5f0f\u3092\u7acb\u3066\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u6307\u6570 1 \u306e\u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f\u304c\u5f97\u3089\u308c\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&#038; \\frac{U_e(t)}{R_0} &#8211; \\frac{U_1}{R_0} + C_1(U_2&#8242; &#8211; U_1&#8242;) = 0 \\\\<br \/>\n&#038; \\frac{U_b}{R_2} &#8211; U_2(\\frac{1}{R_1} + \\frac{1}{R_2}) + C_1(U_1&#8242; &#8211; U_2&#8242;) -0.01f(U_2 &#8211; U_3) = 0 \\\\<br \/>\n&#038; f(U_2 &#8211; U_3) &#8211; \\frac{U_3}{R_3} &#8211; C_2U_3&#8242; = 0 \\\\<br \/>\n&#038; \\frac{U_b}{R_4} &#8211; \\frac{U_4}{R_4} + C_3(U_5&#8242; &#8211; U_4&#8242;) -0.99f(U_2 &#8211; U_3) = 0 \\\\<br \/>\n&#038; -\\frac{U_5}{R_5} + C_3(U_4&#8242; &#8211; U_5&#8242;) = 0 \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\u3053\u3053\u3067 \\(f(U)\\) \u3068 \\(U_e(t)\\) \u306f\u6b21\u306e\u5024\u3092\u4f7f\u7528\u3059\u308b\u3082\u306e\u3068\u3059\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&#038; f(U) = 10^{-6}(e^{\\frac{U}{0.026}} &#8211; 1) \\\\<br \/>\n&#038; U_e(t) = 0.4 sin(200 \\pi t) \\\\<br \/>\n\\end{align}<br \/>\n\\]\n\u3053\u308c\u3092 \\(Mu&#8217; = \\phi(u)\\) \u578b\u306e\u554f\u984c\u3068\u3057\u3066\u8868\u3059\u3068, M, u&#8217; \u304a\u3088\u3073 \\(\\phi(u)\\) \u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308b.<br \/>\n\\[<br \/>\nM =<br \/>\n\\begin{pmatrix}<br \/>\n-C_1 &#038; C_1 \\\\<br \/>\nC_1 &#038; -C_1 \\\\<br \/>\n &#038; &#038; -C_2 \\\\<br \/>\n &#038; &#038; &#038; -C_3 &#038; C_3 \\\\<br \/>\n &#038; &#038; &#038; C_3 &#038; -C_3 \\\\<br \/>\n\\end{pmatrix}<br \/>\n\\]\n\\[<br \/>\nu&#8217; =<br \/>\n\\begin{pmatrix}<br \/>\nU_1&#8242; \\\\<br \/>\nU_2&#8242; \\\\<br \/>\nU_3&#8242; \\\\<br \/>\nU_4&#8242; \\\\<br \/>\nU_5&#8242; \\\\<br \/>\n\\end{pmatrix}<br \/>\n\\]\n\\[<br \/>\n\\phi(u) =<br \/>\n\\begin{pmatrix}<br \/>\n-\\frac{U_e(t)}{R_0} + \\frac{U_1}{R_0} \\\\<br \/>\n-\\frac{U_b}{R_2} + U_2(\\frac{1}{R_1} + \\frac{1}{R_2}) + 0.01f(U_2 &#8211; U_3) \\\\<br \/>\n-f(U_2 + U_3) &#8211; \\frac{U_3}{R_3} \\\\<br \/>\n-\\frac{U_b}{R_4} + \\frac{U_4}{R_4} + 0.99f(U_2 &#8211; U_3) \\\\<br \/>\n\\frac{U_5}{R_5} \\\\<br \/>\n\\end{pmatrix}<br \/>\n\\]\n\u3053\u306e\u5f0f\u306b\u3088\u308b \\(t = 0 \\sim 0.2\\) \u306b\u304a\u3051\u308b\u5165\u529b\u4fe1\u53f7 \\(U_e(t)\\) \u306b\u5bfe\u3059\u308b\u51fa\u529b\u4fe1\u53f7 \\(U_5(t)\\) \u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308b. \u521d\u671f\u5024\u306f, \\(U_1 = 0, \\space U_2 = 3, \\space U_3 = 3, \\space U_4 = 6, \\space U_5 = 0 \\) \u3068\u3057\u305f.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_28_exp11.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5800\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_28_exp11.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_28_exp11-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>\u30c8\u30e9\u30f3\u30b8\u30b9\u30bf\u56de\u8def\u306b\u3088\u308b\u5897\u5e45\u4f5c\u7528\u304c\u78ba\u8a8d\u3067\u304d\u308b.<\/p>\n<p>\\(Mu&#8217; = \\phi(u)\\) \u578b\u306e DAE \u306b\u9069\u7528\u3067\u304d\u308b Radaua, Rodasa \u304a\u3088\u3073 Seulexa \u3092\u7528\u3044\u3066\u8a08\u7b97\u3057\u6bd4\u8f03\u3092\u884c\u3046. \\(Tol (\u8981\u6c42\u7cbe\u5ea6) = 10^{-6}, 10^{-7}, \\dots, 10^{-15}\\) \u3068\u5909\u5316\u3055\u305b\u3066\u8a08\u7b97\u3057\u305f\u3068\u304d\u306b\u5f97\u3089\u308c\u305f \\(t = 10\\) \u306b\u304a\u3051\u308b\u4e0a\u56f3\u306e 6 \u70b9\u306e\u5024\u306e\u76f8\u5bfe\u8aa4\u5dee\u306e\u5e73\u5747\u306b\u5bfe\u3059\u308b\u95a2\u6570\u8a55\u4fa1\u56de\u6570\u3092\u4e21\u5bfe\u6570\u30d7\u30ed\u30c3\u30c8\u3059\u308b. \u76f8\u5bfe\u8aa4\u5dee\u306e\u5e73\u5747\u306f\u53f3\u306b\u3044\u304f\u307b\u3068\u5c11\u306a\u3044 (\u7cbe\u5ea6\u304c\u3088\u3044).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_29_exp11_1.png\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-5801\" srcset=\"https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_29_exp11_1.png 640w, https:\/\/www.ktech.biz\/jp\/wp-content\/uploads\/sites\/2\/2026\/07\/10-4_29_exp11_1-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/p>\n<p>\u306a\u304a, \\(y_1 = U_1 &#8211; U_2, \\space y_2 = U_3, \\space y_3 = U_4 &#8211; U_5, \\space z_1 = U_2, \\space z_2 = U_5\\) \u3068\u304a\u304f\u3068, \u6b21\u306e\u3088\u3046\u306b\u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f\u306e\u4e00\u822c\u5f62 (\\(y&#8217; = f(t, y, z), \\space 0 = g(t, y, z)\\)) \u306b\u5909\u5f62\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u308b.<br \/>\n\\[<br \/>\n\\begin{align}<br \/>\n&#038; y_1&#8242; = \\frac{U_e(t) &#8211; y_1 + z_1}{R_0C_1} \\\\<br \/>\n&#038; y_2&#8242; = \\frac{f(z_1 &#8211; y_2) -\\frac{y_2}{R_3}}{C_2} \\\\<br \/>\n&#038; y_3&#8242; = \\frac{z_2}{R_5C_3} \\\\<br \/>\n&#038; 0 = \\frac{U_e(t) &#8211; y_1 &#8211; z_1}{R_0} + \\frac{U_b}{R_2} &#8211; z_1(\\frac{1}{R_1} + \\frac{1}{R_2}) &#8211; 0.01f(z_1 &#8211; y_2) \\\\<br \/>\n&#038; 0 = \\frac{U_b &#8211; y_3 &#8211; z_2}{R_4} &#8211; \\frac{z_2}{R_5} &#8211; 0.99f(z_1 &#8211; y_2) \\\\<br \/>\n\\end{align}<br 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