{"id":4699,"date":"2014-01-17T06:00:40","date_gmt":"2014-01-16T21:00:40","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=4699"},"modified":"2014-09-10T16:45:01","modified_gmt":"2014-09-10T07:45:01","slug":"post-4699","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=4699","title":{"rendered":"\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u305f\u3081\u306e\u6570\u5024\u89e3\u6cd5"},"content":{"rendered":"<div class=\"theContentWrap-ccc\"><p>\u3000\u6b21\u306e\u5883\u754c\u5024\u554f\u984c\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u3057\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+dy%2Fdx+%3D+f%28x%2C+y%29%5C+%5C+%5C+y%28x_0%29+%3D+y_0%5C+%5C+%5C+%281%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle dy\/dx = f(x, y)\\ \\ \\ y(x_0) = y_0\\ \\ \\ (1)' title='\\displaystyle dy\/dx = f(x, y)\\ \\ \\ y(x_0) = y_0\\ \\ \\ (1)' class='latex' \/><\/p>\n<p>\u6050\u3089\u304f\u6b63\u78ba\u306a\u89e3\u3092\u5f97\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u3067\u3057\u3087\u3046\uff0e\u3053\u306e\u3088\u3046\u306a\u5834\u5408\uff0c\u69d8\u3005\u306a\u65b9\u6cd5\u3067\u8fd1\u4f3c\u5024\u3084\u6570\u5024\u89e3\u6cd5\u304c\u5f97\u3089\u308c\u307e\u3059\uff0e\u3044\u304f\u3064\u304b\u306e\u65b9\u6cd5\u3092\u5217\u6319\u3057\u307e\u3059\uff0e<\/p>\n<ol>\n<li>\u9010\u6b21\u8fd1\u4f3c\u6cd5\u307e\u305f\u306f\u30aa\u30a4\u30e9\u30fc\u6cd5<\/li>\n<li>\u30c6\u30a4\u30e9\u30fc\u7d1a\u6570\u6cd5<\/li>\n<li>\u30d4\u30ab\u30fc\u30eb\u6cd5<\/li>\n<li>\u30eb\u30f3\u30b2\u30af\u30c3\u30bf\u6cd5<\/li>\n<\/ol>\n<h2>1. \u9010\u6b21\u8fd1\u4f3c\u6cd5\u307e\u305f\u306f\u30aa\u30a4\u30e9\u30fc\u6cd5<\/h2>\n<p>\u3000\u3053\u306e\u624b\u6cd5\u3067\u306f\u5fae\u5206\u65b9\u7a0b\u5f0f (1) \u3092\u6b21\u306e\u8fd1\u4f3c\u5f0f\u3067\u7f6e\u63db\u3057\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Cfrac%7By%28x_0+%2B+h%29-y%28x_0%29%7D%7Bh%7D+%3D+f%28x_0%2C+y_0%29%5C+%5C+%5C+%282%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\frac{y(x_0 + h)-y(x_0)}{h} = f(x_0, y_0)\\ \\ \\ (2)' title='\\displaystyle \\frac{y(x_0 + h)-y(x_0)}{h} = f(x_0, y_0)\\ \\ \\ (2)' class='latex' \/><\/p>\n<p>\u305d\u306e\u305f\u3081\uff0c<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+y%28x_0+%2B+h%29+%3D+y%28x_0%29+%2B+hf%28x_0%2C+y_0%29%5C+%5C+%5C+%283%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle y(x_0 + h) = y(x_0) + hf(x_0, y_0)\\ \\ \\ (3)' title='\\displaystyle y(x_0 + h) = y(x_0) + hf(x_0, y_0)\\ \\ \\ (3)' class='latex' \/><\/p>\n<p>\u3053\u306e\u3088\u3046\u306a\u9023\u7d9a\u6027\u306b\u3088\u308a <img src='https:\/\/s0.wp.com\/latex.php?latex=y%28x_0+%2B+2h%29%2C%5C+y%28x_0+%2B+3h%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='y(x_0 + 2h),\\ y(x_0 + 3h)' title='y(x_0 + 2h),\\ y(x_0 + 3h)' class='latex' \/> \u7b49\u3092\u898b\u51fa\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff0e\u5341\u5206\u306b\u5c0f\u3055\u306a <img src='https:\/\/s0.wp.com\/latex.php?latex=h&#038;bg=T&#038;fg=000000&#038;s=0' alt='h' title='h' class='latex' \/> \u3092\u9078\u3076\u3053\u3068\u3067\u826f\u3044\u8fd1\u4f3c\u304c\u5f97\u3089\u308c\u307e\u3059\uff0e<\/p>\n<p>\u3000\u3053\u306e\u65b9\u6cd5\u306e\u5909\u6cd5\u3082\u307e\u305f\u7528\u3044\u3089\u308c\u3066\u3044\u307e\u3059\uff0e<\/p>\n<h2>2. \u30c6\u30a4\u30e9\u30fc\u7d1a\u6570\u6cd5<\/h2>\n<p>\u3000(1) \u306b\u304a\u3051\u308b\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u9023\u7d9a\u3057\u3066\u5fae\u5206\u3059\u308b\u3053\u3068\u3067 <img src='https:\/\/s0.wp.com\/latex.php?latex=y%27%28x_0%29%2C%5C+y%27%27%28x_0%29%2C%5C+y%27%27%27%28x_0%29%2C%5Ccdots&#038;bg=T&#038;fg=000000&#038;s=0' alt='y&#039;(x_0),\\ y&#039;&#039;(x_0),\\ y&#039;&#039;&#039;(x_0),\\cdots' title='y&#039;(x_0),\\ y&#039;&#039;(x_0),\\ y&#039;&#039;&#039;(x_0),\\cdots' class='latex' \/> \u304c\u5f97\u3089\u308c\u307e\u3059\uff0e\u305d\u3057\u3066\u305d\u306e\u89e3\u306f\uff0c\u305d\u306e\u7d1a\u6570\u304c\u53ce\u675f\u3059\u308b\u3053\u3068\u3092\u524d\u63d0\u306b\uff0c\u6b21\u306e\u30c6\u30a4\u30e9\u30fc\u7d1a\u6570\u3067\u5f97\u3089\u308c\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+y%28x%29+%3D+y%28x_0%29+%2B+y%27%28x_0%29%28x+-+x_0%29+%2B+%5Cfrac%7By%27%27%28x_0%29%28x+-+x_0%29%5E2%7D%7B2%21%7D+%2B+%5Ccdots%5C+%5C+%5C+%284%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle y(x) = y(x_0) + y&#039;(x_0)(x - x_0) + \\frac{y&#039;&#039;(x_0)(x - x_0)^2}{2!} + \\cdots\\ \\ \\ (4)' title='\\displaystyle y(x) = y(x_0) + y&#039;(x_0)(x - x_0) + \\frac{y&#039;&#039;(x_0)(x - x_0)^2}{2!} + \\cdots\\ \\ \\ (4)' class='latex' \/><\/p>\n<p>\u7d1a\u6570\u304c\u53ce\u675f\u3059\u308b\u306a\u3089\u3044\u304b\u306a\u308b\u7cbe\u5ea6\u3067\u3082 <img src='https:\/\/s0.wp.com\/latex.php?latex=y%28x_0+%2B+h%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='y(x_0 + h)' title='y(x_0 + h)' class='latex' \/> \u304c\u5f97\u3089\u308c\u307e\u3059\uff0e<\/p>\n<h2>3. \u30d4\u30ab\u30fc\u30eb\u6cd5<\/h2>\n<p>\u3000(1) \u306e\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u7a4d\u5206\u3057\uff0c\u5883\u754c\u6761\u4ef6\u3092\u7528\u3044\u308b\u3053\u3068\u3067\u6b21\u5f0f\u304c\u5f97\u3089\u308c\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+y%28x%29+%3D+y_0+%2B+%5Cint%5E%7Bx%7D_%7Bx_0%7D%5C%21+f%28u%2C+y%29du%5C+%5C+%5C+%285%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle y(x) = y_0 + \\int^{x}_{x_0}\\! f(u, y)du\\ \\ \\ (5)' title='\\displaystyle y(x) = y_0 + \\int^{x}_{x_0}\\! f(u, y)du\\ \\ \\ (5)' class='latex' \/><\/p>\n<p>\u8fd1\u4f3c\u5f0f <img src='https:\/\/s0.wp.com\/latex.php?latex=y_1%28x%29+%3D+y_0&#038;bg=T&#038;fg=000000&#038;s=0' alt='y_1(x) = y_0' title='y_1(x) = y_0' class='latex' \/> \u3092\u524d\u63d0\u3068\u3057\u3066 (5) \u304b\u3089\u6b21\u306e\u65b0\u3057\u3044\u8fd1\u4f3c\u5f0f\u304c\u5f97\u3089\u308c\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+y_2%28x%29+%3D+y_0+%2B+%5Cint%5E%7Bx%7D_%7Bx_0%7D%5C%21+f%28u%2C+y_1%29du%5C+%5C+%5C+%286%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle y_2(x) = y_0 + \\int^{x}_{x_0}\\! f(u, y_1)du\\ \\ \\ (6)' title='\\displaystyle y_2(x) = y_0 + \\int^{x}_{x_0}\\! f(u, y_1)du\\ \\ \\ (6)' class='latex' \/><\/p>\n<p>(5) \u306b\u304a\u3044\u3066\u3053\u308c\u3092\u7528\u3044\u308b\u3068\u5225\u306e\u8fd1\u4f3c\u5f0f\u304c\u5f97\u3089\u308c\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+y_3%28x%29+%3D+y_0+%2B+%5Cint%5E%7Bx%7D_%7Bx_0%7D%5C%21+f%28u%2C+y_2%29du%5C+%5C+%5C+%287%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle y_3(x) = y_0 + \\int^{x}_{x_0}\\! f(u, y_2)du\\ \\ \\ (7)' title='\\displaystyle y_3(x) = y_0 + \\int^{x}_{x_0}\\! f(u, y_2)du\\ \\ \\ (7)' class='latex' \/><\/p>\n<p>\u3000\u3053\u306e\u3088\u3046\u306b\u9023\u7d9a\u3057\u3066\u4e00\u9023\u306e\u8fd1\u4f3c\u5f0f <img src='https:\/\/s0.wp.com\/latex.php?latex=y_1%2C+y_2%2C+y_3%2C%5Ccdots&#038;bg=T&#038;fg=000000&#038;s=0' alt='y_1, y_2, y_3,\\cdots' title='y_1, y_2, y_3,\\cdots' class='latex' \/> \u3092\u5f97\u307e\u3059\uff0e\u3053\u306e\u4e00\u9023\u306e\u8fd1\u4f3c\u5f0f\u306e\u6975\u9650\u306f\uff0c\u3082\u3057\u5b58\u5728\u3059\u308b\u306a\u3089\uff0c\u6c42\u3081\u3089\u308c\u308b\u89e3\u3067\u3059\uff0e\u3057\u304b\u3057\u306a\u304c\u3089\u6570\u56de\u306e\u624b\u9806\u3092\u884c\u3046\u3053\u3068\u3067\u826f\u3044\u8fd1\u4f3c\u304c\u5f97\u3089\u308c\u307e\u3059\uff0e<\/p>\n<h2>4. \u30eb\u30f3\u30b2\u30af\u30c3\u30bf\u6cd5<\/h2>\n<p>\u3000\u3053\u306e\u624b\u6cd5\u306f\u6b21\u306e\u8a08\u7b97\u3092\u542b\u307f\u307e\u3059\uff0e<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+%5Cleft.%5Cbegin%7Barray%7D%7Brcl%7Dk_1+%26+%3D+%26+hf%28x_0%2C+y_0%29+%5C%5C+k_2+%26+%3D+%26+hf%28x_0+%2B+%5Cfrac%7B1%7D%7B2%7Dh%2C+y_0+%2B+%5Cfrac%7B1%7D%7B2%7Dk_1%29+%5C%5C+k_3+%26+%3D+%26+hf%28x_0+%2B+%5Cfrac%7B1%7D%7B2%7Dh%2C+y_0+%2B+%5Cfrac%7B1%7D%7B2%7Dk_2+%5C%5C+k_4+%26+%3D+%26+hf%28x_0+%2B+%5Cfrac%7B1%7D%7B2%7Dh%2C+y_0+%2B+%5Cfrac%7B1%7D%7B2%7Dk_3%29+%5Cend%7Barray%7D+%5Cright%5C%7D%5C+%5C+%5C+%288%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle \\left.\\begin{array}{rcl}k_1 &amp; = &amp; hf(x_0, y_0) \\\\ k_2 &amp; = &amp; hf(x_0 + \\frac{1}{2}h, y_0 + \\frac{1}{2}k_1) \\\\ k_3 &amp; = &amp; hf(x_0 + \\frac{1}{2}h, y_0 + \\frac{1}{2}k_2 \\\\ k_4 &amp; = &amp; hf(x_0 + \\frac{1}{2}h, y_0 + \\frac{1}{2}k_3) \\end{array} \\right\\}\\ \\ \\ (8)' title='\\displaystyle \\left.\\begin{array}{rcl}k_1 &amp; = &amp; hf(x_0, y_0) \\\\ k_2 &amp; = &amp; hf(x_0 + \\frac{1}{2}h, y_0 + \\frac{1}{2}k_1) \\\\ k_3 &amp; = &amp; hf(x_0 + \\frac{1}{2}h, y_0 + \\frac{1}{2}k_2 \\\\ k_4 &amp; = &amp; hf(x_0 + \\frac{1}{2}h, y_0 + \\frac{1}{2}k_3) \\end{array} \\right\\}\\ \\ \\ (8)' class='latex' \/><\/p>\n<p>\u3000\u3086\u3048\u306b<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+y%28x_0+%2B+h%29+%3D+y_0+%2B+%5Cfrac%7B1%7D%7B6%7D%28k_1+%2B+2k_2+%2B+2k_3+%2B+k_4%29%5C+%5C+%5C+%289%29&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle y(x_0 + h) = y_0 + \\frac{1}{6}(k_1 + 2k_2 + 2k_3 + k_4)\\ \\ \\ (9)' title='\\displaystyle y(x_0 + h) = y_0 + \\frac{1}{6}(k_1 + 2k_2 + 2k_3 + k_4)\\ \\ \\ (9)' class='latex' \/><\/p>\n<p>\u3000\u3053\u308c\u3089\u306e\u624b\u6cd5\u3082\u307e\u305f\u6570\u500b\u306e1\u968e\u306e\u5fae\u5206\u65b9\u7a0b\u5f0f\u3068\u3057\u3066\u8a18\u8ff0\u3059\u308b\u3053\u3068\u3067\u9ad8\u968e\u306e\u5fae\u5206\u65b9\u7a0b\u5f0f\u306b\u9069\u5408\u3057\u3066\u3044\u307e\u3059\uff0e<\/p>\n<p><iframe src=\"\/\/rcm-fe.amazon-adsystem.com\/e\/cm?lt1=_blank&#038;bc1=000000&#038;IS2=1&#038;bg1=FFFFFF&#038;fc1=000000&#038;lc1=0000FF&#038;t=fujiitoshiki-22&#038;o=9&#038;p=8&#038;l=as4&#038;m=amazon&#038;f=ifr&#038;ref=ss_til&#038;asins=0071635408\" style=\"width:120px;height:240px;\" scrolling=\"no\" marginwidth=\"0\" marginheight=\"0\" frameborder=\"0\"><\/iframe><\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>\u3000\u6b21\u306e\u5883\u754c\u5024\u554f\u984c\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u3057\u307e\u3059\uff0e \u6050\u3089\u304f\u6b63\u78ba\u306a\u89e3\u3092\u5f97\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u3067\u3057\u3087\u3046\uff0e\u3053\u306e\u3088\u3046\u306a\u5834\u5408\uff0c\u69d8\u3005\u306a\u65b9\u6cd5\u3067\u8fd1\u4f3c\u5024\u3084\u6570\u5024\u89e3\u6cd5\u304c\u5f97\u3089\u308c\u307e\u3059\uff0e\u3044\u304f\u3064\u304b\u306e\u65b9\u6cd5\u3092\u5217\u6319\u3057\u307e\u3059\uff0e \u9010\u6b21\u8fd1\u4f3c\u6cd5\u307e\u305f\u306f\u30aa\u30a4\u30e9\u30fc\u6cd5 \u30c6\u30a4\u30e9\u30fc\u7d1a\u6570\u6cd5 \u30d4\u30ab &hellip; <a href=\"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=4699\" class=\"more-link\"><span class=\"screen-reader-text\">&#8220;\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u305f\u3081\u306e\u6570\u5024\u89e3\u6cd5&#8221; \u306e<\/span>\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":1,"featured_media":6040,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[9],"tags":[],"class_list":["post-4699","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/4699","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4699"}],"version-history":[{"count":7,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/4699\/revisions"}],"predecessor-version":[{"id":6793,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/4699\/revisions\/6793"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/media\/6040"}],"wp:attachment":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4699"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4699"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4699"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}