1 \u968e\u306e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306f\u6b21\u306e\u5f62\u306b\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u308b.
\n\\[
\n y’ = f(t, y(t))
\n\\]\n\u3053\u3053\u3067, \\(y(t)\\) \u306f\u672a\u77e5\u306e\u95a2\u6570\u3067\u3042\u308b. \u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u521d\u671f\u5024\u554f\u984c (initial value problem) \u306f, \u521d\u671f\u70b9 \\(t_0\\) \u306b\u304a\u3051\u308b\u95a2\u6570\u5024 \\(y(t_0)\\) \u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d, \u6700\u7d42\u70b9 \\(t_f\\) \u306b\u304a\u3051\u308b\u5024 \\(y(t_f)\\) \u3092\u6c42\u3081\u308b\u554f\u984c\u3067\u3042\u308b. \u521d\u671f\u70b9\u306b\u304a\u3051\u308b\u95a2\u6570\u5024\u3092\u4e0e\u3048\u308b\u6b21\u5f0f\u306f\u521d\u671f\u6761\u4ef6 (initial condition) \u3068\u3088\u3070\u308c\u308b.
\n\\[
\n y(t_0) = y_0
\n\\]\n
1 \u968e\u306e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u521d\u671f\u5024\u554f\u984c\u306f, \u30b9\u30ab\u30e9\u30fc \\(y\\) \u3092\u30d9\u30af\u30c8\u30eb \\(\\boldsymbol{y}\\) \u306b\u5909\u3048\u3066\u305d\u306e\u307e\u307e\u9023\u7acb\u65b9\u7a0b\u5f0f\u306b\u62e1\u5f35\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b.
\n\\[
\n\\begin{align}
\n& \\boldsymbol{y’} = \\boldsymbol{f}(t, \\boldsymbol{y}) \\\\
\n& \\boldsymbol{y}(t_0) = \\boldsymbol{y_0} \\\\
\n\\end{align}
\n\\]\n\u4f8b\u3048\u3070, 2 \u5909\u6570 (\u30d9\u30af\u30c8\u30eb\u306e\u8981\u7d20\u6570\u304c 2) \u306e\u5834\u5408\u306b\u3064\u3044\u3066\u66f8\u304d\u4e0b\u3059\u3068\u6b21\u306e\u3088\u3046\u306b\u306a\u308b.
\n\\[
\n\\begin{align}
\n& y_1′ = f_1(t, y_1, y_2) \\\\
\n& y_2′ = f_2(t, y_1, y_2) \\\\
\n\\end{align}
\n\\]\n\u3053\u306e\u5834\u5408, \u521d\u671f\u6761\u4ef6\u3082 2 \u3064\u5fc5\u8981\u306b\u306a\u308b.
\n\\[
\n\\begin{align}
\n& y_1(t_0) = {y_1}_0 \\\\
\n& y_2(t_0) = {y_2}_0 \\\\
\n\\end{align}
\n\\]\n
2 \u968e\u306e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306f 1 \u968e\u306e\u9023\u7acb\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u5f62\u306b\u3057\u3066\u6271\u3046\u3053\u3068\u304c\u3067\u304d\u308b. \u4f8b\u3048\u3070, \u6b21\u306e\u65b9\u7a0b\u5f0f\u3092\u8003\u3048\u308b.
\n\\[
\n y” = f(t, y, y’)
\n\\]\n\u3053\u308c\u306f, \\(y_1 = y\\), \\(y_2 = y’\\) \u3068\u304a\u3051\u3070, \u6b21\u306e\u3088\u3046\u306b 1 \u968e\u306e\u9023\u7acb\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306b\u306a\u308b.
\n\\[
\n\\begin{align}
\n& y_1′ = y_2 \\\\
\n& y_2′ = f(t, y_1, y_2) \\\\
\n\\end{align}
\n\\]\n\u3053\u306e\u5834\u5408, 2\u3064\u306e\u521d\u671f\u6761\u4ef6\u304c\u5fc5\u8981\u306b\u306a\u308b.
\n\\[
\n\\begin{align}
\n& y_1(t_0) = y(t_0) = y_0 \\\\
\n& y_2(t_0) = y'(t_0) = y_0′ \\\\
\n\\end{align}
\n\\]\n\u540c\u69d8\u306b\u3057\u3066\u3055\u3089\u306b\u9ad8\u968e\u306e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3053\u3068\u3082\u3067\u304d\u308b.<\/p>\n
\u306a\u304a, \u6b21\u306e\u3088\u3046\u306a\u7279\u5225\u306a\u5f62\u3092\u3057\u305f 2 \u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f (\\(f\\) \u304c \\(y’\\) \u306b\u4f9d\u5b58\u3057\u306a\u3044\u5834\u5408) \u306b\u3064\u3044\u3066\u306f 1 \u968e\u306e\u9023\u7acb\u65b9\u7a0b\u5f0f\u306b\u5909\u63db\u305b\u305a\u306b\u76f4\u63a5\u89e3\u304f\u65b9\u6cd5\u304c\u3042\u308a, 10.2.7 \u3067\u8aac\u660e\u3059\u308b.
\n\\[
\n\\begin{align}
\n& y^{\\prime\\prime} = f(t, y) \\\\
\n& y(t_0) = y_0, y'(t_0) = y_0′ \\space (\u521d\u671f\u6761\u4ef6) \\\\
\n\\end{align}
\n\\]\n
10.1 \u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u521d\u671f\u5024\u554f\u984c\u306e\u57fa\u672c\u6570\u5024\u89e3\u6cd5<\/a> \u306f\u3058\u3081\u306b \u521d\u671f\u5024\u554f\u984c 1 \u968e\u306e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306f\u6b21\u306e\u5f62\u306b\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u308b. \\[ y’ = f(t, y(t)) \\] \u3053\u3053\u3067, \\(y(t)\\) \u306f\u672a\u77e5\u306e\u95a2\u6570\u3067\u3042\u308b. \u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u521d\u671f\u5024\u554f\u984c (initial […]<\/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-5513","post","type-post","status-publish","format-standard","hentry","category-num"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\t
\n10.2 \u30b9\u30c6\u30c3\u30d7\u5e45\u306e\u81ea\u52d5\u8abf\u7bc0, \u5bc6\u51fa\u529b, 2 \u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f<\/a>
\n10.3 \u30b9\u30c6\u30a3\u30d5\u306a\u65b9\u7a0b\u5f0f, \u5fae\u5206\u4ee3\u6570\u65b9\u7a0b\u5f0f<\/a>
\n10.4 \u5b9f\u7528\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u30d9\u30f3\u30c1\u30de\u30fc\u30af<\/a><\/p>\n\u672c\u7ae0\u306e\u53c2\u8003\u6587\u732e<\/h4>\n[1] \u4e00\u677e\u4fe1\u300c\u6570\u5024\u89e3\u6790\u300d(1982) \u671d\u5009\u66f8\u5e97
\n[2] \u540d\u53d6\u4eae\u300c\u6570\u5024\u89e3\u6790\u3068\u305d\u306e\u5fdc\u7528\u300d(1990) \u30b3\u30ed\u30ca\u793e
\n[3] \u4e09\u4e95\u658c\u53cb\u300c\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3\u6cd5\u300d(2003) \u5ca9\u6ce2\u66f8\u5e97
\n[4] 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
\n[5] 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[6] 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<\/p>\n","protected":false},"excerpt":{"rendered":"