{"id":3021,"date":"2020-06-25T20:37:19","date_gmt":"2020-06-25T11:37:19","guid":{"rendered":"https:\/\/www.ktech.biz\/jp\/?p=3021"},"modified":"2021-01-14T11:02:10","modified_gmt":"2021-01-14T02:02:10","slug":"10-ode-4","status":"publish","type":"post","link":"https:\/\/www.ktech.biz\/jp\/num\/10-ode-4\/","title":{"rendered":"10. \u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (4) \u5b9f\u7528\u30eb\u30fc\u30c1\u30f3\u306e\u30d9\u30f3\u30c1\u30de\u30fc\u30af"},"content":{"rendered":"

\u76ee\u6b21<\/h3>\n

\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (1)<\/a>: \u6982\u8981, \uff11\u6bb5\u6cd5, \u591a\u6bb5\u6cd5, \u4f7f\u308f\u308c\u306a\u304f\u306a\u3063\u305f\u89e3\u6cd5
\n\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (2)<\/a>: \u8aa4\u5dee\u306e\u63a8\u5b9a, \u88dc\u5916\u6cd5, \u30b9\u30c6\u30c3\u30d7\u5e45\u306e\u81ea\u52d5\u8abf\u7bc0, \u5bc6\u51fa\u529b, 2\u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f, \u9045\u5ef6\u5fae\u5206\u65b9\u7a0b\u5f0f
\n\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (3)<\/a>: \u89e3\u6cd5\u306e\u5b89\u5b9a\u6027, \u30b9\u30c6\u30a3\u30d5\u306a\u65b9\u7a0b\u5f0f, \u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f
\n\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (4): \u5b9f\u7528\u30eb\u30fc\u30c1\u30f3\u306e\u30d9\u30f3\u30c1\u30de\u30fc\u30af (\u5b9f\u7528\u30eb\u30fc\u30c1\u30f3\u306e\u9078\u629e, \u30b9\u30c6\u30a3\u30d5\u3067\u306f\u306a\u3044\u554f\u984c, \u30b9\u30c6\u30a3\u30d5\u306a\u554f\u984c, \u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f)<\/p>\n

\u5b9f\u7528\u30eb\u30fc\u30c1\u30f3\u306e\u9078\u629e<\/span>\u30b9\u30c6\u30a3\u30d5\u3067\u306a\u3044\u554f\u984c<\/span>\u30b9\u30c6\u30a3\u30d5\u306a\u554f\u984c<\/span>\u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f<\/span><\/div>
\n

\u5b9f\u7528\u30eb\u30fc\u30c1\u30f3\u306e\u9078\u629e<\/h2>\n

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\u3084\u7279\u8a18\u4e8b\u9805\u3092\u53c2\u8003\u306b\u9078\u629e\u3059\u308b\u3068\u3088\u3044. \u30b9\u30c6\u30a3\u30d5\u3067\u306f\u306a\u3044\u554f\u984c\u306b\u30b9\u30c6\u30a3\u30d5\u306a\u554f\u984c\u7528\u306e\u30eb\u30fc\u30c1\u30f3\u3092\u4f7f\u7528\u3057\u3066\u3082\u89e3\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u304c\u52b9\u7387\u304c\u975e\u5e38\u306b\u60aa\u304f\u306a\u308b.<\/p>\n

XLPack\u306b\u53ce\u9332\u3055\u308c\u3066\u3044\u308b\u30eb\u30fc\u30c1\u30f3 (\u30b9\u30c6\u30a3\u30d5\u3067\u306f\u306a\u3044\u554f\u984c\u7528)<\/h3>\n
\n\n\n\n\n\n\n\n\n\n\n\n\n
\u30eb\u30fc\u30c1\u30f3\u540d<\/th>\n\u89e3\u6cd5<\/th>\n\u30b9\u30c6\u30c3\u30d7\u5e45\u81ea\u52d5\u8abf\u7bc0<\/th>\n\u5bc6\u51fa\u529b<\/th>\n\u7279\u8a18\u4e8b\u9805<\/th>\n<\/tr>\n
Derkf<\/td>\n5(4)\u6b21 \u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u30fb\u30d5\u30a7\u30fc\u30eb\u30d9\u30eb\u30b0\u6cd5<\/td>\n\u3007<\/td>\n\u3007<\/td>\nRKF45\u3068\u540c\u7b49<\/td>\n<\/tr>\n
Dopri5<\/td>\n5(4)\u6b21 \u30c9\u30eb\u30de\u30f3\u30fb\u30d7\u30ea\u30f3\u30b9\u6cd5<\/td>\n\u3007<\/td>\n\u3007<\/td>\n<\/td>\n<\/tr>\n
Dverk<\/td>\n6(5)\u6b21 \u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u30fb\u30f4\u30a1\u30fc\u30ca\u30fc\u6cd5<\/td>\n\u3007<\/td>\n\u3007<\/td>\n<\/td>\n<\/tr>\n
Dop853<\/td>\n8(5,3)\u6b21 \u30c9\u30eb\u30de\u30f3\u30fb\u30d7\u30ea\u30f3\u30b9\u6cd5<\/td>\n\u3007<\/td>\n\u3007<\/td>\n<\/td>\n<\/tr>\n
Deabm<\/td>\n1\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\u3007<\/td>\n\u25b3<\/td>\n\u88dc\u9593\u53ef\u80fd\u306a\u5834\u5408\u306f\u88dc\u9593\u5024\u3092\u8fd4\u3059<\/td>\n<\/tr>\n
Odex<\/td>\n\u88dc\u5916\u6cd5 (GBS\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0)<\/td>\n\u3007<\/td>\n\u3007<\/td>\n<\/td>\n<\/tr>\n
Doprin<\/td>\n7(6)\u6b21\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u30fb\u30cb\u30e5\u30b9\u30c8\u30ec\u30e0\u6cd5<\/td>\n\u3007<\/td>\n\u00d7<\/td>\n2\u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (y” = f(t, y)) \u7528<\/td>\n<\/tr>\n
Odex2<\/td>\n\u88dc\u5916\u6cd5 (GBS\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0)<\/td>\n\u3007<\/td>\n\u3007<\/td>\n2\u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (y” = f(t, y)) \u7528<\/td>\n<\/tr>\n
Retard<\/td>\n5(4)\u6b21 \u30c9\u30eb\u30de\u30f3\u30fb\u30d7\u30ea\u30f3\u30b9\u6cd5<\/td>\n\u3007<\/td>\n\u3007<\/td>\n\u9045\u5ef6\u5fae\u5206\u65b9\u7a0b\u5f0f(DDE)\u7528<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\u203b\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”_r”\u306e\u30b5\u30d5\u30a3\u30c3\u30af\u30b9\u304c\u4ed8\u304f)<\/p>\n

XLPack\u306b\u53ce\u9332\u3055\u308c\u3066\u3044\u308b\u30eb\u30fc\u30c1\u30f3 (\u30b9\u30c6\u30a3\u30d5\u306a\u554f\u984c\u7528)<\/h3>\n
\n\n\n\n\n\n\n\n\n\n\n
\u30eb\u30fc\u30c1\u30f3\u540d<\/th>\n\u89e3\u6cd5<\/th>\n\u30b9\u30c6\u30c3\u30d7\u5e45\u81ea\u52d5\u8abf\u7bc0<\/th>\n\u5bc6\u51fa\u529b<\/th>\n\u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f(DAE)\u306b\u4f7f\u7528\u53ef<\/th>\n\u7279\u8a18\u4e8b\u9805<\/th>\n<\/tr>\n
Debdf<\/td>\n1\u301c5\u6b21 \u5f8c\u9000\u5fae\u5206\u516c\u5f0f (BDF)<\/td>\n\u3007<\/td>\n\u25b3<\/td>\n\u00d7<\/td>\nLSODE\u3068\u540c\u7b49
\u88dc\u9593\u53ef\u80fd\u306a\u5834\u5408\u306f\u88dc\u9593\u5024\u3092\u8fd4\u3059<\/td>\n<\/tr>\n
Radau5<\/td>\n5\u6b21\u306e\u9670\u7684\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5 (\u30e9\u30c0\u30a6IIA\u6cd5)<\/td>\n\u3007<\/td>\n\u3007<\/td>\nMy’ = f(t, y) \u6307\u65703\u4ee5\u4e0b<\/td>\n<\/td>\n<\/tr>\n
Radaup<\/td>\n5, 9, 13\u6b21\u306e\u9670\u7684\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5 (\u30e9\u30c0\u30a6IIA\u6cd5)<\/td>\n\u3007<\/td>\n\u3007<\/td>\nMy’ = f(t, y) \u6307\u65703\u4ee5\u4e0b<\/td>\n\u6b21\u6570\u6307\u5b9a\u53ef\u80fd<\/td>\n<\/tr>\n
Radau<\/td>\n5, 9, 13\u6b21\u306e\u9670\u7684\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5 (\u30e9\u30c0\u30a6IIA\u6cd5)<\/td>\n\u3007<\/td>\n\u3007<\/td>\nMy’ = f(t, y) \u6307\u65703\u4ee5\u4e0b<\/td>\n\u6b21\u6570\u3092\u81ea\u52d5\u9078\u629e<\/td>\n<\/tr>\n
Rodas<\/td>\n4(3)\u6b21 \u30ed\u30fc\u30bc\u30f3\u30d6\u30ed\u30c3\u30af\u6cd5<\/td>\n\u3007<\/td>\n\u3007<\/td>\nMy’ = f(t, y) \u6307\u65701<\/td>\n<\/td>\n<\/tr>\n
Seulex<\/td>\n\u88dc\u5916\u6cd5 (\u7dda\u5f62\u9670\u7684\u30aa\u30a4\u30e9\u30fc\u6cd5)<\/td>\n\u3007<\/td>\n\u3007<\/td>\nMy’ = f(t, y) \u6307\u65701<\/td>\n<\/td>\n<\/tr>\n
Dassl<\/td>\n1\u301c5\u6b21 \u5f8c\u9000\u5fae\u5206\u516c\u5f0f (BDF)<\/td>\n\u3007<\/td>\n\u00d7<\/td>\nf(t, y, y’) = 0 \u6307\u65701<\/td>\n\u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f(DAE)\u7528<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\u203b\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”_r”\u306e\u30b5\u30d5\u30a3\u30c3\u30af\u30b9\u304c\u4ed8\u304f)
\n<\/div>\n
\n\u3053\u3053\u306e\u4f8b\u984c\u306e\u8a73\u7d30\u306f\u3059\u3079\u3066[1]\u3092\u53c2\u7167\u306e\u3053\u3068.<\/p>\n

\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\u308bDop853\u3068\u30a2\u30c0\u30e0\u30b9\u30fb\u30d0\u30b7\u30e5\u30d5\u30a9\u30fc\u30b9\u30fb\u30e2\u30eb\u30c8\u30f3\u6cd5\u306eDeabm\u304c\u901f\u3044. \u307e\u305f, \u88dc\u5916\u6cd5\u306eOdex\u3082\u60aa\u304f\u306a\u3044\u3088\u3046\u3067\u3042\u308b. \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\u3066\u307f\u305f\u304c\u95a2\u6570\u306e\u5909\u5316\u304c\u6fc0\u3057\u3044\u3088\u3046\u306a\u5b9f\u8df5\u554f\u984c\u3067\u306f\u82e6\u3057\u3044\u3088\u3046\u3067\u3042\u308b.<\/p>\n

\u30b9\u30c6\u30a3\u30d5\u3067\u306f\u306a\u3044\u554f\u984c<\/h2>\n

\u525b\u4f53\u306e\u56de\u8ee2\u306b\u5bfe\u3059\u308b\u30aa\u30a4\u30e9\u30fc\u65b9\u7a0b\u5f0f<\/h3>\n

\u525b\u4f53\u306e\u56de\u8ee2\u306b\u5bfe\u3059\u308b\u30aa\u30a4\u30e9\u30fc\u65b9\u7a0b\u5f0f\u306f\u6b21\u306e\u3068\u304a\u308a.<\/p>\n

  \r\n  I1<\/sub>y1<\/sub>' = (I2<\/sub> - I3<\/sub>)y2<\/sub>y3<\/sub>\r\n  I2<\/sub>y2<\/sub>' = (I3<\/sub> - I1<\/sub>)y3<\/sub>y1<\/sub>\r\n  I3<\/sub>y3<\/sub>' = (I1<\/sub> - I2<\/sub>)y1<\/sub>y2<\/sub> + f(x)\r\n\r\n<\/pre>\n
 
\ny1<\/sub>, y2<\/sub>, y3<\/sub> \u306f\u56de\u8ee2\u30d9\u30af\u30c8\u30eb\u306e\u5ea7\u6a19, I1<\/sub>, I2<\/sub>, I3<\/sub> \u306f\u4e3b\u6163\u6027\u30e2\u30fc\u30e1\u30f3\u30c8\u3067\u3042\u308b. \u7b2c3\u5ea7\u6a19\u306b\u306f\u6b21\u306e\u5916\u90e8\u5f37\u5236\u529b\u304c\u52a0\u308f\u3063\u3066\u3044\u308b.<\/p>\n
  \r\n  f(x) = 0.25 sin2<\/sup>x  (3\u03c0 \u2266 x \u2266 4\u03c0)\r\n         0  (\u305d\u306e\u4ed6\u306ex)\r\n\r\n<\/pre>\n
 
\n\u521d\u671f\u5024\u306f I1<\/sub> = 0.5, I2<\/sub> = 2, I3<\/sub> = 3, y1<\/sub>(0) = 1, y2<\/sub>(0) = 0, y3<\/sub>(0) = 0.9 \u3067\u3042\u308b.<\/p>\n
\"\"<\/p>\n
\u3053\u308c\u3092, Derkf, Dopri5, Dverk, Dop853, Deabm \u304a\u3088\u3073 Odex \u3092\u7528\u3044\u3066 Tol(\u8981\u6c42\u7cbe\u5ea6) = 10-6<\/sup>, 10-7<\/sup>, …, 10-15<\/sup> \u3068\u5909\u5316\u3055\u305b\u3066\u8a08\u7b97\u3057\u305f\u3068\u304d\u306b\u5f97\u3089\u308c\u305f t = 20 \u306b\u304a\u3051\u308b y1<\/sub>, y2<\/sub>, y3<\/sub> \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\u3057\u305f\u3082\u306e\u3067\u3042\u308b. \u8aa4\u5dee\u306f\u53f3\u306b\u3044\u304f\u307b\u3068\u5c11\u306a\u3044(\u7cbe\u5ea6\u304c\u3088\u3044). \u6bd4\u8f03\u306e\u305f\u3081\u30aa\u30a4\u30e9\u30fc\u6cd5(Euler)\u30684\u6b21\u306e\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5(RK4)\u3082\u8868\u793a\u3057\u305f. \u3053\u3061\u3089\u306f h = 0.01, 0.005, …, 10-5<\/sup> \u3068\u5909\u5316\u3055\u305b\u3066\u8a08\u7b97\u3057\u305f.<\/p>\n
\"\"<\/p>\n
\u4ed6\u306e\u554f\u984c\u3067\u3082\u305d\u3046\u3067\u3042\u308b\u304c, Tol = 10-13<\/sup>, 10-14<\/sup>, 10-15<\/sup> \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. \u30eb\u30fc\u30c1\u30f3\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\u306e\u3067\u6ce8\u610f\u304c\u5fc5\u8981\u3060\u308d\u3046.<\/p>\n
\u3053\u306e\u554f\u984c\u306f4\u6b21\u306e\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5\u306f\u5c11\u3057\u5909\u306a\u52d5\u304d\u3092\u793a\u3057\u3066\u3044\u308b\u304c\u7cbe\u5ea610-11<\/sup>\u4ed8\u8fd1\u307e\u3067\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\u6642\u9593\u306f\u304b\u304b\u308b\u304c\u6b63\u3057\u304f\u8a08\u7b97\u3067\u304d\u305d\u3046\u3067\u3042\u308b.<\/p>\n
\u30ed\u30fc\u30ec\u30f3\u30c4\u65b9\u7a0b\u5f0f<\/h3>\n
\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.<\/p>\n
  \r\n  y1<\/sub>' = -\u03c3y1<\/sub> + \u03c3y2<\/sub>\r\n  y2<\/sub>' = -y1<\/sub>y3<\/sub> + ry1<\/sub> - y2<\/sub>\r\n  y3<\/sub>' = y1<\/sub>y2<\/sub> - by3<\/sub>\r\n\r\n<\/pre>\n
 
\n\u30b6\u30eb\u30c4\u30de\u30f3\u306e\u5024 \u03c3 = 10, r = 28, b = 8\/3 \u3092\u4f7f\u3046\u3068\u975e\u5468\u671f\u7684\u306b\u306a\u308b. \u521d\u671f\u5024\u306f y1<\/sub>(0) = -8, y2<\/sub>(0) = 8, y3<\/sub>(0) = 27 \u3067\u3042\u308b. \u6b21\u306e\u3088\u3046\u306a\u30ed\u30fc\u30ec\u30f3\u30c4\u30fb\u30a2\u30c8\u30e9\u30af\u30bf\u3068\u3088\u3070\u308c\u308b\u56f3\u5f62\u306b\u306a\u308b.<\/p>\n
\"\"<\/p>\n
\u4e0a\u3068\u540c\u69d8\u306b, Derkf, Dopri5, Dverk, Dop853, Deabm \u304a\u3088\u3073 Odex \u306e\u7d50\u679c\u3092\u793a\u3059. \u6bd4\u8f03\u306e\u305f\u3081\u30aa\u30a4\u30e9\u30fc\u6cd5(Euler)\u30684\u6b21\u306e\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5(RK4)\u3082\u8868\u793a\u3057\u305f. t = 16 \u306b\u304a\u3051\u308b\u76f8\u5bfe\u8aa4\u5dee\u306e\u5e73\u5747\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u305f.<\/p>\n
\"\"<\/p>\n
\u3053\u306e\u554f\u984c\u306f\u7cbe\u5ea6\u304c\u51fa\u306b\u304f\u304f, 10-7<\/sup>\uff5e10-8<\/sup>\u4ed8\u8fd1\u3067\u9650\u754c\u306e\u3088\u3046\u3067\u3042\u308b.<\/p>\n
4\u6b21\u306e\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5\u3067\u306f\u554f\u984c\u306a\u304f\u8a08\u7b97\u3067\u304d\u305f\u304c, \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
\u30a2\u30ec\u30f3\u30b9\u30c8\u30fc\u30d5\u8ecc\u9053<\/h3>\n
\u5236\u9650\u4e09\u4f53\u554f\u984c\u306e\u4f8b\u3067\u3042\u308b. \u8cea\u91cf\u304c\u03bc\u3068\u03bc'(= 1 – \u03bc)\u306e2\u3064\u306e\u5929\u4f53\u304c\u5e73\u9762\u5185\u56de\u8ee2\u904b\u52d5\u3092\u3057\u3066\u304a\u308a, \u305d\u306e2\u3064\u306b\u6bd4\u3079\u3066\u8cea\u91cf\u304c\u7121\u8996\u3067\u304d\u308b\u7b2c3\u306e\u7269\u4f53\u304c\u540c\u4e00\u5e73\u9762\u5185\u3092\u904b\u52d5\u3059\u308b.<\/p>\n
  \r\n  y1<\/sub>'' = y1<\/sub> + 2y2<\/sub>' - \u03bc'(y1<\/sub> + \u03bc)\/D1<\/sub> - \u03bc(y1<\/sub> - \u03bc')\/D2<\/sub>\r\n  y2<\/sub>'' = y2<\/sub> - 2y1<\/sub>' - \u03bc'y2<\/sub>\/D1<\/sub> - \u03bcy2<\/sub>\/D2<\/sub>\r\n  D1<\/sub> = ((y1<\/sub> + \u03bc)2<\/sup> + y2<\/sub>2<\/sup>)3\/2<\/sup>\r\n  D2<\/sub> = ((y1<\/sub> - \u03bc')2<\/sup> + y2<\/sub>2<\/sup>)3\/2<\/sup>\r\n  \u03bc = 0.012277471, \u03bc' = 1 - \u03bc\r\n\r\n<\/pre>\n
 
\n\u6b21\u306e\u521d\u671f\u5024\u3092\u7528\u3044\u308b\u3068, t = 17.0652165601579625588917206249 \u3067\u5468\u671f\u89e3\u3068\u306a\u308b\u3053\u3068\u304c\u77e5\u3089\u308c\u3066\u3044\u308b.<\/p>\n
  \r\n  y1<\/sub>(0) = 0.994, y1<\/sub>'(0) = 0\r\n  y2<\/sub>(0) = 0, y2<\/sub>'(0) = -2.00158510637908252240537862224\r\n\r\n<\/pre>\n
 
\n\u3053\u308c\u306f\u30a2\u30ec\u30f3\u30b9\u30c8\u30fc\u30d5\u8ecc\u9053\u3068\u3088\u3070\u308c\u3066\u3044\u308b. 1\u5468\u671f\u5206\u3092\u4ee5\u4e0b\u306b\u793a\u3059.<\/p>\n
\"\"<\/p>\n
2\u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306a\u306e\u3067\u5909\u6570\u5909\u63db\u3057\u30662\u500d\u306e\u5143\u6570\u306e1\u968e\u306e\u9023\u7acb\u65b9\u7a0b\u5f0f\u306b\u3057\u3066\u89e3\u304f. \u4e0a\u3068\u540c\u69d8\u306b, Derkf, Dopri5, Dverk, Dop853, Deabm \u304a\u3088\u3073 Odex \u306e\u7d50\u679c\u3092\u793a\u3059. \u6bd4\u8f03\u306e\u305f\u3081\u30aa\u30a4\u30e9\u30fc\u6cd5(Euler)\u30684\u6b21\u306e\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5(RK4)\u3082\u8868\u793a\u3057\u305f. 1\u5468\u671f\u5f8c\u306e\u76f8\u5bfe\u8aa4\u5dee\u306e\u5e73\u5747\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u305f.<\/p>\n
\"\"<\/p>\n
4\u6b21\u306e\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5\u306e\u7d50\u679c\u3092\u898b\u308b\u3068\u672c\u6765Derkf(RKF45)\u3088\u308a\u5c11\u3057\u60aa\u3044\u7a0b\u5ea6\u306e\u306f\u305a\u3060\u304c\u306f\u308b\u304b\u306b\u591a\u304f\u306e(100\u500d\u7a0b\u5ea6\u306e)\u95a2\u6570\u8a08\u7b97\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\u306f\u30b9\u30c6\u30c3\u30d7\u5e45\u306e\u81ea\u52d5\u8abf\u7bc0\u6a5f\u80fd\u304c\u306a\u3044\u3068\u82e6\u3057\u3044\u3088\u3046\u3067\u3042\u308b.<\/p>\n
\u30a2\u30ec\u30f3\u30b9\u30c8\u30fc\u30d5\u8ecc\u9053 (2)<\/h3>\n
\u30a2\u30ec\u30f3\u30b9\u30c8\u30fc\u30d5\u8ecc\u9053\u306f\u56fa\u5b9a\u5ea7\u6a19\u7cfb\u3067\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\n
  \r\n  y1<\/sub>'' = \u03bc'(a1<\/sub>(x) - y1<\/sub>)\/D1<\/sub> + \u03bc(b1<\/sub>(x) - y1<\/sub>)\/D2<\/sub>\r\n  y2<\/sub>'' = \u03bc'(a2<\/sub>(x) - y2<\/sub>)\/D1<\/sub> + \u03bc(b2<\/sub>(x) - y2<\/sub>)\/D2<\/sub>\r\n  D1<\/sub> = ((y1<\/sub> - a1<\/sub>(x))2<\/sup> + (y2<\/sub> - a2<\/sub>(x))2<\/sup>)3\/2<\/sup>\r\n  D2<\/sub> = ((y1<\/sub> - b1<\/sub>(x))2<\/sup> + (y2<\/sub> - b2<\/sub>(x))2<\/sup>)3\/2<\/sup>\r\n  a1<\/sub>(x) = -\u03bccos(x), a2<\/sub>(x) = -\u03bcsin(x)\r\n  b1<\/sub>(x) = \u03bc'cos(x), b2<\/sub>(x) = \u03bc'sin(x)\r\n  \u03bc = 0.012277471, \u03bc' = 1 - \u03bc\r\n\r\n<\/pre>\n
 
\n\u521d\u671f\u5024\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\n
  \r\n  y1<\/sub>(0) = 0.994, y1<\/sub>'(0) = 0\r\n  y2<\/sub>(0) = 0, y2<\/sub>'(0) = -2.00158510637908252240537862224 + 0.994\r\n\r\n<\/pre>\n
 
\n\u3053\u306e\u8ecc\u9053\u306f\u91cd\u306a\u3063\u3066\u308f\u304b\u308a\u306b\u304f\u3044\u304c, 1\u5468\u671f\u5206\u3092\u793a\u3059\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\n
\"\"<\/p>\n
\u3053\u306e\u65b9\u7a0b\u5f0f\u306f y” = f(t, y) \u306e\u5f62\u306e2\u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306a\u306e\u3067, \u3053\u306e\u5f62\u5c02\u7528\u306e\u88dc\u5916\u6cd5\u30eb\u30fc\u30c1\u30f3Odex2\u304c\u4f7f\u3048\u308b. \u6bd4\u8f03\u5bfe\u8c61\u3068\u3057\u3066\u306f\u901a\u5e38\u306eOdex\u306e\u4ed6\u306bDoprin\u3068Rknint(\u3053\u308c\u3089\u306fXLPack\u306b\u306f\u542b\u307e\u308c\u3066\u3044\u306a\u3044)\u3092\u4f7f\u3046. Doprin\u306f7(6)\u6b21\u57cb\u3081\u8fbc\u307f\u578b\u30cb\u30e5\u30b9\u30c8\u30ec\u30e0\u6cd5[3], Rknint\u306f6(4)\u6b21 \u307e\u305f\u306f 12(10)\u6b21\u57cb\u3081\u8fbc\u307f\u578b\u30cb\u30e5\u30b9\u30c8\u30ec\u30e0\u6cd5[4]\u306e\u30b9\u30c6\u30c3\u30d7\u5e45\u306e\u81ea\u52d5\u8abf\u7bc0\u6a5f\u80fd\u4ed8\u304d\u30eb\u30fc\u30c1\u30f3\u3067\u3042\u308b.<\/p>\n
\u6bd4\u8f03\u306e\u305f\u3081\u306b4\u6b21\u306e\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5(RK4), 4\u6b21\u306e\u30cb\u30e5\u30b9\u30c8\u30ec\u30e0\u6cd5(NY4)\u304a\u3088\u30735\u6b21\u306e\u30cb\u30e5\u30b9\u30c8\u30ec\u30e0\u6cd5(NY5)\u306e\u7d50\u679c\u3082\u793a\u3057\u305f.<\/p>\n
\"\"<\/p>\n
Odex2\u306f\u4e88\u5b9a\u901a\u308aOdex\u306e\u7d04\u534a\u5206\u306e\u95a2\u6570\u8a08\u7b97\u3067\u89e3\u3092\u6c42\u3081\u3066\u3044\u308b. \u57cb\u3081\u8fbc\u307f\u578b\u30cb\u30e5\u30b9\u30c8\u30ec\u30e0\u6cd5\u3068\u6bd4\u8f03\u3057\u3066\u3082\u905c\u8272\u306a\u3044.<\/p>\n
\u4e0a\u306e\u56de\u8ee2\u5ea7\u6a19\u7cfb\u306e\u5834\u5408\u3068\u540c\u3058\u3067, \u30b9\u30c6\u30c3\u30d7\u5e45\u306e\u81ea\u52d5\u8abf\u7bc0\u6a5f\u80fd\u304c\u306a\u3044RK4, NY4, NY5\u306f\u591a\u304f\u306e\u95a2\u6570\u8a08\u7b97\u3092\u5fc5\u8981\u3068\u3057\u305f.<\/p>\n
\u6587\u732e[3] E. Hairer, S.P. Norsett and G. Wanner, “Solving Ordinary Differential Equations I”, Springer Series in Computational Mathematics, Springer-Verlag (1987) [\u6587\u732e[1]\u306e\u65e7\u7248]\n
\u6587\u732e[4] R.W. Brankin, I. Gladwell, J.R. Dormand, P.J. Prince & W.L. Seward (1989): Algorithm 670. A Runge-Kutta-Nystrom code. ACM Trans. Math. Softw., Vol.15, p.31-40.<\/p>\n
\u5929\u6587\u529b\u5b66\u306e\u554f\u984c<\/h3>\n
\u5ea7\u6a19\u3068\u8cea\u91cf\u304c\u305d\u308c\u305e\u308c (xi<\/sub>, yi<\/sub>), mi<\/sub> = i (i = 1, …, 7) \u306e7\u500b\u306e\u661f\u306e\u5e73\u9762\u5185\u306e\u904b\u52d5\u3067\u3042\u308b.<\/p>\n
  \r\n  xi<\/sub>'' = \u03a3 mj<\/sub>(xj<\/sub>) - xi<\/sub>)\/rij<\/sub> (\u03a3\u306f j \u2260 i)\r\n  yi<\/sub>'' = \u03a3 mj<\/sub>(yj<\/sub>) - yi<\/sub>)\/rij<\/sub> (\u03a3\u306f j \u2260 i)\r\n  rij<\/sub> = ((xj<\/sub>) - xi<\/sub>)2<\/sup> + (yj<\/sub>) - yi<\/sub>)2<\/sup>)3\/2<\/sup> (i, j = 1, ..., 7)\r\n\r\n<\/pre>\n
 
\n\u521d\u671f\u5024\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3042\u308b.<\/p>\n
  \r\n  x1<\/sub>(0) = 3, x2<\/sub>(0) = 3, x3<\/sub>(0) = -1, x4<\/sub>(0) = -3, \r\n  x5<\/sub>(0) = 2, x6<\/sub>(0) = -2, x7<\/sub>(0) = 2,\r\n  y1<\/sub>(0) = 3, y2<\/sub>(0) = -3, y3<\/sub>(0) = 2, y4<\/sub>(0) = 0, \r\n  y5<\/sub>(0) = 0, y6<\/sub>(0) = -4, y7<\/sub>(0) = 4,\r\n  x6<\/sub>'(0) = 1.75, x7<\/sub>'(0) = -1.5, y4<\/sub>'(0) = -1.25, y5<\/sub>'(0) = 1, \r\n  xi<\/sub>'(0) = yi<\/sub>'(0) = 0 (\u305d\u306e\u4ed6\u306ei)\r\n\r\n<\/pre>\n
 
\nt = 0, 0.1, 0.2, …, 3 \u3092\u30d7\u30ed\u30c3\u30c8\u3059\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\n
\"\"<\/p>\n
2\u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306a\u306e\u3067\u5909\u6570\u5909\u63db\u3057\u30661\u968e\u306e2\u500d\u306e\u5143\u6570\u306e14\u5143\u9023\u7acb\u65b9\u7a0b\u5f0f\u306b\u3057\u3066\u89e3\u304f. \u4e0a\u3068\u540c\u69d8\u306b, Derkf, Dopri5, Dverk, Dop853, Deabm \u304a\u3088\u3073 Odex \u306e\u7d50\u679c\u3092\u793a\u3059. \u6bd4\u8f03\u306e\u305f\u3081\u30aa\u30a4\u30e9\u30fc\u6cd5(Euler)\u30684\u6b21\u306e\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5(RK4)\u3082\u8868\u793a\u3057\u305f. t = 3 \u306b\u304a\u3051\u308b7\u3064\u306e\u5ea7\u6a19\u306e\u76f8\u5bfe\u8aa4\u5dee\u306e\u5e73\u5747\u3092\u30d7\u30ed\u30c3\u30c8\u3057\u305f.<\/p>\n
\"\"<\/p>\n
\u3053\u306e\u65b9\u7a0b\u5f0f\u306f y” = f(t, y) \u306e\u5f62\u306e2\u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306a\u306e\u3067, \u3053\u306e\u5f62\u5c02\u7528\u306e\u88dc\u5916\u6cd5\u30eb\u30fc\u30c1\u30f3Odex2\u304c\u4f7f\u3048\u308b. \u6bd4\u8f03\u5bfe\u8c61\u3068\u3057\u3066\u306f\u901a\u5e38\u306eOdex\u306e\u4ed6\u306bDoprin\u3068Rknint\u3092\u8868\u793a\u3057\u305f. Doprin\u306f7(6)\u6b21\u57cb\u3081\u8fbc\u307f\u578b\u30cb\u30e5\u30b9\u30c8\u30ec\u30e0\u6cd5, Rknint\u306f6(4)\u6b21 \u307e\u305f\u306f 12(10)\u6b21\u57cb\u3081\u8fbc\u307f\u578b\u30cb\u30e5\u30b9\u30c8\u30ec\u30e0\u6cd5\u306e\u30b9\u30c6\u30c3\u30d7\u5e45\u306e\u81ea\u52d5\u8abf\u7bc0\u6a5f\u80fd\u4ed8\u304d\u30eb\u30fc\u30c1\u30f3\u3067\u3042\u308b(\u30a2\u30ec\u30f3\u30b9\u30c8\u30fc\u30d5\u8ecc\u9053 (2) \u3092\u53c2\u7167).<\/p>\n
\u6bd4\u8f03\u306e\u305f\u3081\u306b4\u6b21\u306e\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5(RK4), 4\u6b21\u306e\u30cb\u30e5\u30b9\u30c8\u30ec\u30e0\u6cd5(NY4)\u304a\u3088\u30735\u6b21\u306e\u30cb\u30e5\u30b9\u30c8\u30ec\u30e0\u6cd5(NY5)\u306e\u7d50\u679c\u3082\u793a\u3057\u305f.<\/p>\n
\"\"<\/p>\n
\u3053\u306e\u554f\u984c\u3067\u3082\u30b9\u30c6\u30c3\u30d7\u5e45\u306e\u81ea\u52d5\u8abf\u7bc0\u6a5f\u80fd\u304c\u306a\u3044RK4, NY4, 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
\u611f\u67d3\u30e2\u30c7\u30eb(\u9045\u5ef6\u5fae\u5206\u65b9\u7a0b\u5f0f)<\/h3>\n
\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
\u4eba\u53e3\u306e\u4e2d\u3067 y1<\/sub>(t)\u306f\u611f\u67d3\u53ef\u80fd\u306a\u4eba(susceptible), y2<\/sub>(t)\u306f\u611f\u67d3\u8005(infected), y3<\/sub>(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\u7a4dy1<\/sub>(t)y2<\/sub>(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.<\/p>\n
  \r\n  y1<\/sub>'(t) = -y1<\/sub>(t)y2<\/sub>(t)\r\n  y2<\/sub>'(t) = y1<\/sub>(t)y2<\/sub>(t) -  y2<\/sub>(t)\r\n  y3<\/sub>'(t) = y2<\/sub>(t)\r\n\r\n<\/pre>\n
 
\n\u521d\u671f\u5024\u306f\u6b21\u306e\u3068\u304a\u308a\u3068\u3059\u308b.<\/p>\n
  \r\n  y1<\/sub>(0) = 5, y2<\/sub>(0) = 0.1, y3<\/sub>(0) = 1\r\n\r\n<\/pre>\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>\n
\u3082\u3057\u514d\u75ab\u3092\u6301\u3064\u4eba\u304c\u4e00\u5b9a\u671f\u9593\u03c4\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\u03c42<\/sub>\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.<\/p>\n
  \r\n  y1<\/sub>'(t) = -y1<\/sub>(t)y2<\/sub>(t - \u03c42<\/sub>) + y2<\/sub>(t - \u03c4)\r\n  y2<\/sub>'(t) = y1<\/sub>(t)y2<\/sub>(t - \u03c42<\/sub>) -  y2<\/sub>(t)\r\n  y3<\/sub>'(t) = y2<\/sub>(t) - y2<\/sub>(t - \u03c4)\r\n\r\n<\/pre>\n
 
\n\u03c4 = 10, \u03c42<\/sub> = 1 \u3068\u3057\u3066Retard\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. \u306a\u304a, \u521d\u671f\u5024\u306f\u4e0a\u3068\u540c\u3058\u3067\u3042\u308b\u304c, \u9045\u5ef6\u5fae\u5206\u65b9\u7a0b\u5f0f\u3067\u306ft = -\u03c4 \uff5e 0 \u306e\u5024\u3082\u5fc5\u8981\u306b\u306a\u308b\u306e\u3067\u3053\u3053\u3067\u306f\u521d\u671f\u5024\u306b\u540c\u3058\u3068\u3057\u305f.<\/p>\n
\"\"
\n<\/div>\n
\n\u3053\u3053\u306e\u4f8b\u984c\u306e\u8a73\u7d30\u306f\u3059\u3079\u3066[2]\u3092\u53c2\u7167\u306e\u3053\u3068.<\/p>\n
\u3053\u3053\u3067\u306f\u95a2\u6570\u306e\u547c\u3073\u51fa\u3057\u56de\u6570\u3067\u3057\u304b\u8a55\u4fa1\u3057\u3066\u3044\u306a\u3044\u304c, Debdf (BDF), Radau5 (5\u6b21IRK), Seulex (\u88dc\u5916\u6cd5) \u306f\u540c\u7a0b\u5ea6\u3067\u3042\u3063\u305f. Radau(IRK 5\u6b21\uff5e13\u6b21\u53ef\u5909)\u306f\u9ad8\u6b21\u306e\u516c\u5f0f\u304c\u9078\u629e\u3055\u308c\u308b\u306e\u304b\u4ed6\u3088\u308a\u901f\u3044\u3088\u3046\u3067\u3042\u308b. Rodas (\u30ed\u30fc\u30bc\u30f3\u30d6\u30ed\u30c3\u30af\u6cd5)\u306f\u9045\u3044\u3088\u3046\u306b\u307f\u3048\u308b\u304c\u8a08\u7b97\u91cf\u306f\u591a\u304f\u306a\u3044\u53ef\u80fd\u6027\u304c\u3042\u308b(\u4eca\u56de\u306f\u8a08\u7b97\u91cf\u306b\u3088\u308b\u8a55\u4fa1\u306f\u884c\u3063\u3066\u3044\u306a\u3044).<\/p>\n
\u30b9\u30c6\u30a3\u30d5\u306a\u554f\u984c<\/h2>\n
\u30d5\u30a1\u30f3\u30fb\u30c7\u30eb\u30fb\u30dd\u30eb\u632f\u52d5\u5b50<\/h3>\n
\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f<\/p>\n
  \r\n  y'' + \u03b1y' + y = 0\r\n\r\n<\/pre>\n
 
\n\u306e\u89e3\u306f, \u03b1 > 0 \u306a\u3089\u3070\u6e1b\u8870\u3057, \u03b1 < 0 \u306a\u3089\u3070\u4e0d\u5b89\u5b9a\u306b\u306a\u308b.<\/p>\n
y\u304c\u5c0f\u3055\u3044\u3068\u304d\u306f \u03b1 > 0 \u306b, y\u304c\u5927\u304d\u3044\u3068\u304d\u306f \u03b1 < 0 \u3068\u306a\u308b\u3088\u3046\u306b\u03b1\u3092\u5909\u5316\u3055\u305b\u308b\u305f\u3081\u306b \u03b1 = \u03b5(y2<\/sup> – 1) (\u03b5 > 0) \u3068\u3057, \u3055\u3089\u306b y1<\/sub>‘ = y2<\/sub> \u3068\u304a\u304f\u3068\u6b21\u306e\u9023\u7acb\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u304c\u5f97\u3089\u308c\u308b.<\/p>\n
  \r\n  y1<\/sub>' = y2<\/sub>\r\n  y2<\/sub>' = \u03b5(1 - y1<\/sub>2<\/sup>)y2<\/sub> - y1<\/sub>  (\u03b5 > 0)\r\n\r\n<\/pre>\n
 
\n\u3053\u306e\u65b9\u7a0b\u5f0f\u3067\u306f, \u5c0f\u3055\u3044\u632f\u52d5\u306f\u5897\u5e45\u3055\u308c,\u3000\u5927\u304d\u3044\u632f\u52d5\u306f\u6e1b\u8870\u3055\u308c\u308b. \u5f93\u3063\u3066, \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)\u306e\u5b58\u5728\u304c\u4e88\u60f3\u3055\u308c\u308b. \u03b5 = 1, \u521d\u671f\u5024 y1<\/sub>(0) = 2, y2<\/sub>(0) = -2 \u3092\u59cb\u70b9\u3068\u3057\u3066\u8a08\u7b97\u3059\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u5468\u671f\u8ecc\u9053\u306b\u5165\u3063\u305f.<\/p>\n
\"\"<\/p>\n
\u5404\u30eb\u30fc\u30c1\u30f3\u306e\u6bd4\u8f03\u306e\u305f\u3081\u306b, \u03b5 = 10-6<\/sup>, \u521d\u671f\u5024 y1<\/sub>(0) = 2, y2<\/sub>(0) = 0 \u3068\u3057\u3066\u8a08\u7b97\u3059\u308b. Debdf, Radau5, Radau, Rodas \u304a\u3088\u3073 Seulex \u3092\u7528\u3044\u3066 Tol(\u8981\u6c42\u7cbe\u5ea6) = 10-6<\/sup>, 10-7<\/sup>, …, 10-15<\/sup> \u3068\u5909\u5316\u3055\u305b\u3066\u8a08\u7b97\u3057\u305f\u3068\u304d\u306b\u5f97\u3089\u308c\u305f t = 11 \u306b\u304a\u3051\u308b y1<\/sub> \u304a\u3088\u3073 y2<\/sub> \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. \u8aa4\u5dee\u306f\u53f3\u306b\u3044\u304f\u307b\u3068\u5c11\u306a\u3044(\u7cbe\u5ea6\u304c\u3088\u3044).<\/p>\n
\"\"<\/p>\n
\u30aa\u30ec\u30b4\u30cd\u30fc\u30bf<\/h3>\n
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.<\/p>\n
  \r\n  y1<\/sub>' = 77.27(y2<\/sub> + y1<\/sub>(1 - 8.375\u00d710-6<\/sup>y1<\/sub> - y2<\/sub>))\r\n  y2<\/sub>' = (1\/77.27)(y3<\/sub> - (1 + y1<\/sub>)y2<\/sub>)\r\n  y3<\/sub>' = 0.161(y1<\/sub> - y3<\/sub>)\r\n\r\n<\/pre>\n
 
\n\u521d\u671f\u5024\u306f y1<\/sub>(0) = 1, y2<\/sub>(0) = 2, y3<\/sub>(0) = 3 \u3067\u3042\u308b. t = 360 \u306e\u3068\u304d\u306e\u5024\u3092\u6c42\u3081\u308b. \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>\n
\u4e0a\u3068\u540c\u69d8\u306b, Debdf, Radau5, Radau, Rodas \u304a\u3088\u3073 Seulex \u306e\u7d50\u679c\u3092\u793a\u3059.<\/p>\n
\"\"<\/p>\n
\u30d6\u30e9\u30bb\u30ec\u30fc\u30bf<\/h3>\n
\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
  \r\n            k1<\/sub>\r\n       A  ----->  X\r\n            k2<\/sub>\r\n   B + X  ----->  Y + D (2\u5206\u5b50\u53cd\u5fdc)\r\n            k3<\/sub>\r\n  2X + Y  ----->  3X    (\u81ea\u5df1\u89e6\u5a923\u5206\u5b50\u53cd\u5fdc)\r\n            k4<\/sub>\r\n       X  ----->  E\r\n\r\n<\/pre>\n
 
\nA\u3068B\u306f\u4e00\u5b9a\u5024\u3067\u3042\u308b\u3068\u3057, \u307e\u305f, \u53cd\u5fdc\u901f\u5ea6ki<\/sub>\u3092\u3059\u3079\u30661\u306b\u3059\u308b. u(t) = X(t), v(t) = Y(t) \u3068\u304a\u3051\u3070\u6b21\u5f0f\u304c\u5f97\u3089\u308c\u308b.<\/p>\n
  \r\n  u' = A + u2<\/sup>v - (B + 1)u\r\n  v' = Bu - u2<\/sup>v\r\n\r\n<\/pre>\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.<\/p>\n
  \r\n  \u2202u\/\u2202t = A + u2<\/sup>v - (B + 1)u + \u03b1\u22022<\/sup>u\/\u2202x2<\/sup>\r\n  \u2202v\/\u2202t = Bu - u2<\/sup>v + \u03b1\u22022<\/sup>v\/\u2202x2<\/sup>\r\n\r\n<\/pre>\n
 
\n\u3053\u3053\u3067, 0 \u2266 x \u2266 1, A = 1, B = 3, \u03b1 = 1\/50, \u5883\u754c\u6761\u4ef6, \u521d\u671f\u6761\u4ef6\u306f\u6b21\u306e\u3068\u304a\u308a\u3068\u3059\u308b.<\/p>\n
  \r\n  u(0, t) = u(1, t) = 1, v(0, t) = v(1, t) = 3\r\n  u(x, 0) = 1 + (1\/2)sin(2\u03c0x), v(x, 0) = 3\r\n\r\n<\/pre>\n
 
\nx\u306b\u95a2\u3059\u308b2\u968e\u5fae\u5206\u3092 x1<\/sub> = i\/(N + 1) (1 \u2266 i \u2266 N), \u0394x = 1\/(N + 1) \u306eN\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.<\/p>\n
  \r\n  u' = 1 + ui<\/sub>2<\/sup>vi<\/sub> - 4ui<\/sub> + \u03b1\/(\u0394x)2<\/sup>(ui-1<\/sub> - 2ui<\/sub> + ui+1<\/sub>)\r\n  v' = 3ui<\/sub> - ui<\/sub>2<\/sup>vi<\/sub> + \u03b1\/(\u0394x)2<\/sup>(vi-1<\/sub> - 2vi<\/sub> + vi+1<\/sub>)\r\n\r\n  u0<\/sub>(t) = uN+1<\/sub>(t) = 1, v0<\/sub>(t) = vN+1<\/sub>(t) = 3\r\n  ui<\/sub>(0) = 1 + (1\/2)sin(2\u03c0xi<\/sub>), vi<\/sub>(0) = 3  (i = 1, ..., N)\r\n\r\n<\/pre>\n
 
\nN = 500 \u3068\u3059\u308b\u3068, \u6700\u5927\u56fa\u6709\u5024\u7d04-20000\u3092\u6301\u3064\u30b9\u30c6\u30a3\u30d5\u306a1000\u5143\u306e\u5fae\u5206\u65b9\u7a0b\u5f0f\u7cfb\u306b\u306a\u308b. \u7aef\u4ed8\u8fd1(x\u304c0\u307e\u305f\u306f1\u306b\u8fd1\u3044\u3068\u3053\u308d)\u3068\u4e2d\u592e\u4ed8\u8fd1(x\u304c0.5\u4ed8\u8fd1)\u306e\u5024\u3092\u30d7\u30ed\u30c3\u30c8\u3059\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u3063\u305f.<\/p>\n
\"\"<\/p>\n
\u4e0a\u3068\u540c\u69d8\u306b, Debdf, Radau5, Radau, Rodas \u304a\u3088\u3073 Seulex \u306e\u7d50\u679c\u3092\u793a\u3059. \u8aa4\u5dee\u306f t = 10 \u306b\u304a\u3051\u308b\u4e0a\u56f3\u306e6\u70b9\u306e\u5024\u306e\u76f8\u5bfe\u8aa4\u5dee\u306e\u5e73\u5747\u5024\u3068\u3057\u305f.\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\u4e0b2\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\u5fc5\u8981\u304c\u3042\u308b. \u305d\u3046\u3057\u306a\u3044\u3068\u8a08\u7b97\u91cf\u304c\u81a8\u5927\u306b\u306a\u3063\u3066\u3057\u307e\u3046.<\/p>\n
\"\"<\/p>\n<\/div>\n
\n
\u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f<\/h2>\n
\u5358\u632f\u308a\u5b50<\/h3>\n
\u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f\u306e\u9805\u3067\u4f8b\u3068\u3057\u3066\u4f7f\u7528\u3057\u305f\u5358\u632f\u308a\u5b50\u3092\u76f4\u4ea4\u5ea7\u6a19\u3067\u518d\u3073\u53d6\u308a\u4e0a\u3052\u308b.<\/p>\n
\u4e0b\u56f3\u306e\u3088\u3046\u306b, \u9577\u3055l[m]\u306e\u7cf8\u306b\u91cd\u3055m[kg]\u306e\u304a\u3082\u308a\u304c\u3064\u3044\u305f\u632f\u308a\u5b50\u3092\u8003\u3048\u308b. \u304a\u3082\u308a\u306e\u4f4d\u7f6e\u306f(q1<\/sub>, q2<\/sub>)\u3068\u3059\u308b. g[m\/s2<\/sup>]\u306f\u91cd\u529b\u52a0\u901f\u5ea6\u3067\u3042\u308b.<\/p>\n
\"\"<\/p>\n
\u3053\u306e\u632f\u308a\u5b50\u306e\u904b\u52d5\u306f\u6b21\u306e\u5e38\u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f\u3067\u8868\u3055\u308c\u305f. v1<\/sub>, v2<\/sub>\u306fq1<\/sub>, q2<\/sub>\u65b9\u5411\u306e\u901f\u5ea6\u3067\u3042\u308b.<\/p>\n
  \r\n  q1<\/sub>' = v1<\/sub>\r\n  q2<\/sub>' = v2<\/sub>\r\n  v1<\/sub>' = -\u03bbq1<\/sub>\r\n  v2<\/sub>' = -\u03bbq2<\/sub> - g\r\n  0 = q1<\/sub>2<\/sup> + q2<\/sub>2<\/sup> - l2<\/sup>  [\u6307\u65703]\r\n\r\n<\/pre>\n
 
\n\u3053\u306e\u5f0f\u306f\u6307\u65703\u3067\u3042\u308b. \u6307\u65702\u304a\u3088\u3073\u6307\u65701\u306e\u3068\u304d\u6700\u5f8c\u306e\u5f0f\u306f\u6b21\u306e\u3088\u3046\u3067\u3042\u3063\u305f.<\/p>\n
  \r\n  0 = q1<\/sub>v1<\/sub> + q2<\/sub>v2<\/sub>  [\u6307\u65702]\r\n  0 = -\u03bb - gq2<\/sub> + v1<\/sub>2<\/sup> + v2<\/sub>2<\/sup>  [\u6307\u65701]\r\n\r\n<\/pre>\n
 
\n\u6307\u65701\u306e\u5f0f\u306e\u03bb\u3092\u6700\u521d\u306e4\u3064\u306e\u5f0f\u306b\u4ee3\u5165\u3057\u3066\u5f97\u3089\u308c\u308b\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f(= \u6307\u65700)\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3042\u308b.<\/p>\n
  \r\n  q1<\/sub>' = v1<\/sub>\r\n  q2<\/sub>' = v2<\/sub>\r\n  v1<\/sub>' = (gq2<\/sub> - v1<\/sub>2<\/sup> - v2<\/sub>2<\/sup>)q1<\/sub>\r\n  v2<\/sub>' = (gq2<\/sub> - v1<\/sub>2<\/sup> - v2<\/sub>2<\/sup>)q2<\/sub> - g\r\n\r\n<\/pre>\n
 
\n\u4ee5\u4e0a\u306e\u5f0f\u3092\u4f7f\u3063\u3066 t = 0 (q1<\/sub> = sin(\u03c0\/4), q2<\/sub> = -cos(\u03c0\/4), v1<\/sub> = 0, v2<\/sub> = 0) \u304b\u3089\u59cb\u3081\u30662\u5468\u671f\u5f8c\u306e\u4f4d\u7f6e\u3092\u6c42\u3081\u305d\u306e\u76f8\u5bfe\u8aa4\u5dee\u3068\u95a2\u6570\u8a08\u7b97\u56de\u6570(\u4e0a\u306e5\u672c(\u307e\u305f\u306f4\u672c)\u306e\u5f0f\u3092\u30bb\u30c3\u30c8\u3067\u8a08\u7b97\u3057\u30661\u56de\u3068\u30ab\u30a6\u30f3\u30c8\u3059\u308b)\u3092\u30d7\u30ed\u30c3\u30c8\u3059\u308b. \u306a\u304a, Tol = 1.0e-4, 1.0e-5, …, 1.0e-12 \u3068\u5909\u3048\u3066\u8a08\u7b97\u3057\u305f.<\/p>\n
Radau5, Radau, Rodas, Seulex\u304a\u3088\u3073Dassl\u3092\u4f7f\u7528\u3057\u305f(Radaup\u306f\u5bfe\u8c61\u3068\u3057\u306a\u304b\u3063\u305f\u304cRadau5\u3068Radau\u306e\u7d50\u679c\u306b\u6e96\u3058\u308b\u3068\u8003\u3048\u3066\u3088\u3044). \u6bd4\u8f03\u306e\u305f\u3081\u306b, \u5909\u63db\u3057\u305f\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092Derkf\u3067\u89e3\u3044\u305f\u5834\u5408\u304a\u3088\u3073\u540c\u3058\u304f\u5b89\u5b9a\u5316\u3057\u3066\u89e3\u3044\u305f\u5834\u5408\u3082\u8f09\u305b\u305f.<\/p>\n
Radau5, Radau, Rodas, Seulex\u306f Mu’ = \u03c6(u) \u578b\u306e\u554f\u984c\u3092\u89e3\u304f\u3088\u3046\u306b\u4f5c\u3089\u308c\u3066\u3044\u3066, \u3053\u306e\u5834\u5408M\u3092\u6b21\u306e\u3088\u3046\u306b\u8a2d\u5b9a\u3057\u305f.<\/p>\n
  \r\n      ( 1             )\r\n      (    1          )\r\n  M = (       1       )\r\n      (          1    )\r\n      (             0 )\r\n\r\n<\/pre>\n
 
\n\u6ce8 – \u3053\u308c\u3089\u306e\u30eb\u30fc\u30c1\u30f3\u306f M = I(\u5358\u4f4d\u884c\u5217) \u306e\u3068\u304d\u306f\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u9670\u89e3\u6cd5\u3068\u3057\u3066\u52d5\u4f5c\u3057, M <> I \u3067\u3042\u308c\u3070\u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f.<\/p>\n
Radau5\u3068Radau\u306f\u6307\u65702\u30683\u306b\u9069\u7528\u3059\u308b\u3068\u304d\u306f\u30d1\u30e9\u30e1\u30fc\u30bfNind1, Nind2, Nind3\u3092\u8a2d\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a, \u305d\u308c\u305e\u308c 4, 1, 0 \u304a\u3088\u3073 4, 0, 1 \u3068\u3057\u305f.<\/p>\n
\u6307\u65701\u306e\u5834\u5408<\/h4>\n
\"\"<\/p>\n
Radau5\u3068Radau\u306f Tol = 1.0e-6\u4ee5\u4e0b\u3067\u306f\u30a2\u30f3\u30c0\u30fc\u30d5\u30ed\u30fc\u3067\u505c\u6b62\u3057\u305f. Dassl\u306f Tol = 1.0e-7\u4ee5\u4e0b\u3067\u306f\u53ce\u675f\u305b\u305a\u505c\u6b62\u3057\u305f. Derkf(\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f)\u306e\u5834\u5408, \u5b89\u5b9a\u5316\u3092\u884c\u3046\u3068\u9ad8\u7cbe\u5ea6\u306e\u9818\u57df\u3067\u306f\u304b\u3048\u3063\u3066\u8a08\u7b97\u91cf\u304c\u5897\u3048\u305f\u304c, \u7cbe\u5ea6\u304c\u4f4e\u3044\u3068\u304d\u306b\u306f\u52b9\u679c\u304c\u3042\u3063\u305f.<\/p>\n
\u6307\u65702\u306e\u5834\u5408<\/h4>\n
\"\"<\/p>\n
Seulex\u306f\u6307\u65702\u306f\u9069\u7528\u7bc4\u56f2\u5916\u3067\u3042\u308b\u304c\u89e3\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u305f\u3082\u306e\u306e\u8a08\u7b97\u91cf\u304c\u975e\u5e38\u306b\u591a\u304f\u306a\u3063\u305f. Rodas\u3068Dassl\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
\u6307\u65703\u306e\u5834\u5408<\/h4>\n
\"\"<\/p>\n
\u6307\u65703\u3067\u4f7f\u3048\u308b\u306e\u306fRadau5\u3068Radau\u3067\u3042\u308b\u304c\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306b\u6bd4\u3079\u308b\u3068\u8a08\u7b97\u91cf\u306f\u975e\u5e38\u306b\u591a\u3044.<\/p>\n
\u30c8\u30e9\u30f3\u30b8\u30b9\u30bf\u30fc\u56de\u8def<\/h3>\n
\u6b21\u306e\u30c8\u30e9\u30f3\u30b8\u30b9\u30bf\u30fc\u5897\u5e45\u56de\u8def\u3092\u8003\u3048\u308b. \u56f3\u306e\u4e2d\u3067 1, 2, …, 5 \u306e\u70b9\u306b\u304a\u3051\u308b\u96fb\u5727\u3092 U1<\/sub>, U2<\/sub>, …, U5<\/sub>\u3068\u3059\u308b. Ue<\/sub>(t)\u306f\u5165\u529b\u4fe1\u53f7\u96fb\u5727, Ub<\/sub>\u306f\u96fb\u6e90\u96fb\u5727\u3067\u3042\u308b(Ub<\/sub> = 6V). \u51fa\u529b\u4fe1\u53f7\u306f5\u306b\u304a\u3051\u308b\u96fb\u5727U5<\/sub>\u3068\u3057\u3066\u53d6\u308a\u51fa\u3059\u3053\u3068\u304c\u3067\u304d\u308b.<\/p>\n
\"\"<\/p>\n
f(U)\u3068Ue<\/sub>(t)\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3042\u308b.<\/p>\n
  \r\n  f(U) = 10-6<\/sup>(exp(U\/0.026) - 1)\r\n  Ue<\/sub>(t) = 0.4\u30fbsin(200\u03c0t)\r\n\r\n<\/pre>\n
 
\n\u62b5\u6297R\u3092\u6d41\u308c\u308b\u96fb\u6d41\u306f I = U\/R, \u30b3\u30f3\u30c7\u30f3\u30b5C\u3092\u6d41\u308c\u308b\u96fb\u6d41\u306f I = C\u30fbdU\/dt \u3092\u6e80\u305f\u3059. \u30c8\u30e9\u30f3\u30b8\u30b9\u30bf\u3067\u306f2\u304b\u30893\u306b\u6d41\u308c\u308b\u96fb\u6d41\u304c99\u500d\u5897\u5e45\u3055\u308c\u30664\u304b\u30893\u306b\u6d41\u308c\u308b\u96fb\u6d41\u306b\u306a\u308b\u3082\u306e\u3068\u3057, \u3053\u308c\u3089\u306e\u96fb\u6d41\u306f\u96fb\u4f4d\u5dee U2 – U3 \u306b\u4f9d\u5b58\u3057, \u95a2\u6570f(U2 – 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, 1, 2, …, 5 \u306e\u70b9\u306b\u304a\u3044\u3066\u65b9\u7a0b\u5f0f\u3092\u7acb\u3066\u308b\u3068\u6b21\u306e\u3088\u3046\u306b\u6307\u65701\u306e\u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f\u304c\u5f97\u3089\u308c\u308b.<\/p>\n
  \r\n  Ue<\/sub>(t)\/R0<\/sub> - U1<\/sub>\/R0<\/sub> + C1<\/sub>(U2<\/sub>' - U1<\/sub>') = 0\r\n  Ub<\/sub>\/R2<\/sub> - U2<\/sub>(1\/R1<\/sub> + 1\/R2<\/sub>) + C1<\/sub>(U1<\/sub>' - U2<\/sub>') -0.01f(U2<\/sub> - U3<\/sub>) = 0\r\n  f(U2<\/sub> - U3<\/sub>) - U3<\/sub>\/R3<\/sub> - C2<\/sub>U3<\/sub>' = 0\r\n  Ub<\/sub>\/R4<\/sub> - U4<\/sub>\/R4<\/sub> + C3<\/sub>(U5<\/sub>' - U4<\/sub>') -0.99f(U2<\/sub> - U3<\/sub>) = 0\r\n  -U5<\/sub>\/R5<\/sub> + C3<\/sub>(U4<\/sub>' - U5<\/sub>') = 0\r\n\r\n<\/pre>\n
 
\n\u3053\u308c\u3092 Mu’ = \u03c6(u) \u578b\u306e\u554f\u984c\u3068\u3057\u3066\u8868\u3059\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308b.<\/p>\n
  \r\n      ( -C1<\/sub>  C1<\/sub>             )\r\n      (  C1<\/sub> -C1<\/sub>             )\r\n  M = (         -C2<\/sub>         )\r\n      (             -C3<\/sub>  C3<\/sub> )\r\n      (              C3<\/sub> -C3<\/sub> )\r\n\r\n       ( U1<\/sub>' )\r\n       ( U2<\/sub>' )\r\n  u' = ( U3<\/sub>' )\r\n       ( U4<\/sub>' )\r\n       ( U5<\/sub>' )\r\n\r\n          ( -Ue<\/sub>(t)\/R0<\/sub> + U1<\/sub>\/R0<\/sub>                         )\r\n          ( -Ub<\/sub>\/R2<\/sub> + U2<\/sub>(1\/R1<\/sub> + 1\/R2<\/sub>) + 0.01f(U2<\/sub> - U3<\/sub>) )\r\n  \u03c6(u) = ( -f(U2<\/sub> + U3<\/sub>) - U3<\/sub>\/R3<\/sub>                       )\r\n          ( -Ub<\/sub>\/R4<\/sub> + U4<\/sub>\/R4<\/sub> + 0.99f(U2<\/sub> - U3<\/sub>)           )\r\n          ( U5<\/sub>\/R5<\/sub>                                     )\r\n\r\n<\/pre>\n
 
\nRadau5\u3092\u4f7f\u3063\u3066 t = 0 \uff5e 0.1 \u3092\u8a08\u7b97\u3059\u308b\u3068, \u5165\u529b\u4fe1\u53f7\u3068\u51fa\u529b\u4fe1\u53f7\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u3063\u305f.<\/p>\n
\"\"<\/p>\n
\u306a\u304a, y1<\/sub> = U1<\/sub> – U2<\/sub>, y2<\/sub> = U3<\/sub>, y3<\/sub> = U4<\/sub> – U5<\/sub>, z1<\/sub> = U2<\/sub>, z2<\/sub> = U5<\/sub> \u3068\u304a\u304f\u3068, \u6b21\u306e\u3088\u3046\u306b\u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f\u306e\u4e00\u822c\u5f62 (y’ = f(t, y, z), 0 = g(t, y, z)) \u306b\u5909\u5f62\u3067\u304d\u308b.<\/p>\n
  \r\n  y1<\/sub>' = (Ue<\/sub>(t) - y1<\/sub> + z1<\/sub>)\/(R0<\/sub>C1<\/sub>)\r\n  y2<\/sub>' = (f(z1<\/sub> - y2<\/sub>) -y2<\/sub>\/R3<\/sub>)\/C2<\/sub>\r\n  y3<\/sub>' = z2<\/sub>\/(R5<\/sub>C3<\/sub>)\r\n  0 = (Ue<\/sub>(t) - y1<\/sub> - z1<\/sub>)\/R0<\/sub> + Ub<\/sub>\/R2<\/sub> - z1<\/sub>(1\/R1<\/sub> + 1\/R2<\/sub>) - 0.01f(z1<\/sub> - y2<\/sub>)\r\n  0 = (Ub<\/sub> - y3<\/sub> - z2<\/sub>)\/R4<\/sub> - z2<\/sub>\/R5<\/sub> - 0.99f(z1<\/sub> - y2<\/sub>)\r\n\r\n<\/pre>\n
 
\nRadau5, Radau, Rodas, Seulex\u304a\u3088\u3073Dassl\u3092\u6bd4\u8f03\u3057\u3066\u307f\u308b. t = 0 \u304b\u3089\u59cb\u3081\u3066 t = 0.1 \u306b\u304a\u3051\u308bU5<\/sub>\u306e\u5024\u306e\u76f8\u5bfe\u8aa4\u5dee\u3068\u95a2\u6570\u8a08\u7b97\u56de\u6570\u3092\u30d7\u30ed\u30c3\u30c8\u3059\u308b. \u306a\u304a, Tol = 1.0e-4, 1.0e-5, …, 1.0e-10 \u3068\u5909\u3048\u3066\u8a08\u7b97\u3057\u305f.<\/p>\n
Mu’ = \u03c6(u) \u578b\u306e\u5f0f\u3092\u4f7f\u3063\u305f\u6642\u306e\u7d50\u679c\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3042\u308b.<\/p>\n
\"\"<\/p>\n
\u4e00\u822c\u5f62 (y’ = f(t, y, z), 0 = g(t, y, z)) \u306b\u5909\u5f62\u3057\u305f\u5f0f\u3092\u4f7f\u3046\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u3063\u305f.<\/p>\n
\"\"<\/p>\n
\u4f3c\u305f\u3088\u3046\u306a\u7d50\u679c\u3067\u3042\u308b\u304c, Dassl\u306f\u4e0d\u898f\u5247\u306a\u52d5\u304d\u3092\u793a\u3057\u305f.
\n<\/div><\/div><\/div>\n
\n
\u53c2\u8003\u6587\u732e<\/h4>\n[1] E. Hairer, \u4ed6\u300c\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3\u6cd5 I\u300d(2007) \u30b7\u30e5\u30d7\u30ea\u30f3\u30ac\u30fc\u30fb\u30b8\u30e3\u30d1\u30f3
\n[2] E. Hairer, \u4ed6\u300c\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3\u6cd5 II\u300d(2008) \u30b7\u30e5\u30d7\u30ea\u30f3\u30ac\u30fc\u30fb\u30b8\u30e3\u30d1\u30f3
\n[3] U.M.\u30a2\u30c3\u30b7\u30e3\u30fc, \u4ed6\u300c\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3068\u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3\u6cd5\u300d(2006) \u57f9\u98a8\u9928<\/p>\n","protected":false},"excerpt":{"rendered":"
\u76ee\u6b21 \u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (1): \u6982\u8981, \uff11\u6bb5\u6cd5, \u591a\u6bb5\u6cd5, \u4f7f\u308f\u308c\u306a\u304f\u306a\u3063\u305f\u89e3\u6cd5 \u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (2): \u8aa4\u5dee\u306e\u63a8\u5b9a, \u88dc\u5916\u6cd5, \u30b9\u30c6\u30c3\u30d7\u5e45\u306e\u81ea\u52d5\u8abf\u7bc0, \u5bc6\u51fa\u529b, 2\u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f, \u9045\u5ef6\u5fae\u5206\u65b9\u7a0b\u5f0f \u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (3): […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[13],"tags":[],"class_list":["post-3021","post","type-post","status-publish","format-standard","hentry","category-num"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/posts\/3021","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/comments?post=3021"}],"version-history":[{"count":5,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/posts\/3021\/revisions"}],"predecessor-version":[{"id":3236,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/posts\/3021\/revisions\/3236"}],"wp:attachment":[{"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/media?parent=3021"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/categories?post=3021"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ktech.biz\/jp\/wp-json\/wp\/v2\/tags?post=3021"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}