{"id":4598,"date":"2023-12-18T10:33:35","date_gmt":"2023-12-18T01:33:35","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=4598"},"modified":"2023-12-18T10:37:54","modified_gmt":"2023-12-18T01:37:54","slug":"maxima-%e3%81%a6%e3%82%99%e5%b8%b8%e5%be%ae%e5%88%86%e6%96%b9%e7%a8%8b%e5%bc%8f","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/%e5%8f%82%e8%80%83%ef%bc%9amaxima-%e7%b7%a8\/maxima-%e3%81%ab%e3%82%88%e3%82%8b%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/maxima-%e3%81%a6%e3%82%99%e5%b8%b8%e5%be%ae%e5%88%86%e6%96%b9%e7%a8%8b%e5%bc%8f\/","title":{"rendered":"Maxima \u3066\u3099\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f"},"content":{"rendered":"<p>Maxima \u3067\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3002\u89e3\u6790\u7684\u306b\uff0c\u3042\u308b\u3044\u306f\u6570\u5024\u7684\u306b\u3002<br \/>\n<!--more--><\/p>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5-ode2()\">\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5 <code>ode2()<\/code><\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>Maxima \u306f 1 \u968e\u304a\u3088\u3072\u3099 2 \u968e\u306e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092 <code>ode2<\/code> \u95a2\u6570\u3092\u4f7f\u3063\u3066\u89e3\u304f\u3053\u3068\u304b\u3099\u3066\u3099\u304d\u307e\u3059\u3002<\/p>\n<p>Maxima \u3092\u4f7f\u3063\u3066\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u4f8b\u306b\u3064\u3044\u3066\u306f\uff0c\u7406\u5de5\u7cfb\u306e\u6570\u5b66C \u3067\u3084\u308a\u307e\u3057\u305f\u306e\u3067\uff0c\u8a73\u7d30\u306f\u7701\u7565\u3057\u307e\u3059\u3002\u4ee5\u4e0b\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e7%90%86%e5%b7%a5%e7%b3%bb%e3%81%ae%e6%95%b0%e5%ad%a6c\/\">\u7406\u5de5\u7cfb\u306e\u6570\u5b66C<\/a>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e7%90%86%e5%b7%a5%e7%b3%bb%e3%81%ae%e6%95%b0%e5%ad%a6c\/maxima-jupyter-%e3%81%a6%e3%82%99%e5%b8%b8%e5%be%ae%e5%88%86%e6%96%b9%e7%a8%8b%e5%bc%8f\/\">Maxima-Jupyter \u3066\u3099\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u7df4\u7fd2-2-1\">\u7df4\u7fd2 2-1<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p><strong>\u91cd\u529b\u5834\u4e2d\u306e\u6295\u3051\u3099\u4e0a\u3051\u3099\u904b\u52d5<\/strong><\/p>\n<ol>\n<li>\u9ad8\u3055 $0$ \u304b\u3089\u521d\u901f\u5ea6 $v_0$ \u3066\u3099\u925b\u76f4\u4e0a\u65b9\u306b\u6295\u3051\u3099\u4e0a\u3051\u3099\u305f\u7269\u4f53\u306e\u6642\u523b $t$ \u306b\u304a\u3051\u308b\u9ad8\u3055 $y$ \u3092\u6c42\u3081\u306a\u3055\u3044\u3002\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f\uff0c<br \/>\n$$ \\frac{d^2 y}{dt^2} = -g$$<\/li>\n<li>\u901f\u5ea6\u306b\u6bd4\u4f8b\u3059\u308b\u7a7a\u6c17\u62b5\u6297\u304b\u3099\u3042\u308b\u5834\u5408\uff0c\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u3002<br \/>\n\u3053\u306e\u3068\u304d\uff0c\u9ad8\u3055 $0$ \u304b\u3089\u521d\u901f\u5ea6 $v_0$ \u3066\u3099\u925b\u76f4\u4e0a\u65b9\u306b\u6295\u3051\u3099\u4e0a\u3051\u3099\u305f\u7269\u4f53\u306e\u6642\u523b $t$ \u306b\u304a\u3051\u308b\u9ad8\u3055 $y$ \u3092<br \/>\n\u6c42\u3081\u306a\u3055\u3044\u3002<br \/>\n$$ \\frac{d^2 y}{dt^2} = -g &#8211; \\beta \\frac{dy}{dt}$$<\/li>\n<li>\u524d\u554f 2. \u3066\u3099\u6c42\u3081\u305f\u89e3\u304b\u3099 $\\beta \\rightarrow 0$ \u306e\u3068\u304d\uff0c\u524d\u554f 1. \u306e\u7b54\u3048\u306b\u4e00\u81f4\u3059\u308b\u3053\u3068\u3092\u793a\u3057\u306a\u3055\u3044\u3002<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[1]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* 1. *\/<\/span>\r\n<span class=\"cm\">\/* \u91cd\u529b\u52a0\u901f\u5ea6 g \u306f\u6b63\u306e\u5024 *\/<\/span>\r\n<span class=\"nf\">assume<\/span><span class=\"p\">(<\/span><span class=\"nv\">g<\/span> <span class=\"o\">&gt;<\/span> <span class=\"mi\">0<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"cm\">\/* \u89e3\u304f\u3079\u304d\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092 eom (equation of motion) \u306b\u4ee3\u5165 *\/<\/span>\r\n<span class=\"nv\">eom<\/span><span class=\"o\">:<\/span> <span class=\"o\">'<\/span><span class=\"nf\">diff<\/span><span class=\"p\">(<\/span><span class=\"nv\">y<\/span>, <span class=\"nv\">t<\/span>, <span class=\"mi\">2<\/span><span class=\"p\">)<\/span>  <span class=\"o\">=<\/span> <span class=\"o\">-<\/span><span class=\"nv\">g<\/span>$\r\n\r\n<span class=\"cm\">\/* \u5fae\u5206\u65b9\u7a0b\u5f0f eom \u3092 y \u306b\u3064\u3044\u3066\u89e3\u304f\u3002\u72ec\u7acb\u5909\u6570\u306f t *\/<\/span>\r\n<span class=\"nf\">ode2<\/span><span class=\"p\">(<\/span><span class=\"nv\">eom<\/span>, <span class=\"nv\">y<\/span>, <span class=\"nv\">t<\/span><span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p><code>ode2()<\/code> \u3067\u89e3\u3044\u305f\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u89e3\u306b\u542b\u307e\u308c\u308b $\\%k_1, \\%k_2$ \u306f\u7a4d\u5206\u5b9a\u6570\u3067\u3059\u3002\uff082\u968e\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u89e3\u306b\u306f\u7a4d\u5206\u5b9a\u6570\u304c2\u500b\u3002\uff09<\/p>\n<p>$t=0$ \u306e\u3068\u304d $\\displaystyle y = 0, \\ \\frac{dy}{dt} = v_0$ \u3068\u3044\u3046\u521d\u671f\u6761\u4ef6\u3092\u8ab2\u3057\u3066\u7a4d\u5206\u5b9a\u6570\u3092\u6c7a\u3081\u308b\u4f8b\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[2]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u76f4\u524d\u306e\u89e3 % \u306b\u5bfe\u3057\u3066\u521d\u671f\u6761\u4ef6\u3092 ic2() \u3067\u8ab2\u3057\u307e\u3059\u3002*\/<\/span>\r\n<span class=\"nf\">ic2<\/span><span class=\"p\">(<\/span><span class=\"nv\">%<\/span>, <span class=\"nv\">t<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>, <span class=\"nv\">y<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>, <span class=\"o\">'<\/span><span class=\"nf\">diff<\/span><span class=\"p\">(<\/span><span class=\"nv\">y<\/span>, <span class=\"nv\">t<\/span><span class=\"p\">)<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">v0<\/span><span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[3]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* 2. *\/<\/span>\r\n<span class=\"cm\">\/* \u7a7a\u6c17\u62b5\u6297\u306e\u4fc2\u6570\u306f\u6b63\u306e\u5024 *\/<\/span>\r\n<span class=\"nf\">assume<\/span><span class=\"p\">(<\/span><span class=\"nv\">beta<\/span> <span class=\"o\">&gt;<\/span> <span class=\"mi\">0<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"cm\">\/* \u89e3\u304f\u3079\u304d\u904b\u52d5\u65b9\u7a0b\u5f0f\u3092 eom (equation of motion) \u306b\u4ee3\u5165 *\/<\/span>\r\n<span class=\"nv\">eom<\/span><span class=\"o\">:<\/span> <span class=\"o\">'<\/span><span class=\"nf\">diff<\/span><span class=\"p\">(<\/span><span class=\"nv\">y<\/span>, <span class=\"nv\">t<\/span>, <span class=\"mi\">2<\/span><span class=\"p\">)<\/span>  <span class=\"o\">=<\/span> <span class=\"o\">-<\/span><span class=\"nv\">g<\/span> <span class=\"o\">-<\/span> <span class=\"nv\">beta<\/span> <span class=\"o\">*<\/span> <span class=\"o\">'<\/span><span class=\"nf\">diff<\/span><span class=\"p\">(<\/span><span class=\"nv\">y<\/span>, <span class=\"nv\">t<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"cm\">\/* \u5fae\u5206\u65b9\u7a0b\u5f0f eom \u3092 y \u306b\u3064\u3044\u3066\u89e3\u304f\u3002\u72ec\u7acb\u5909\u6570\u306f t *\/<\/span>\r\n<span class=\"nf\">ode2<\/span><span class=\"p\">(<\/span><span class=\"nv\">eom<\/span>, <span class=\"nv\">y<\/span>, <span class=\"nv\">t<\/span><span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$t=0$ \u306e\u3068\u304d $\\displaystyle y = 0, \\ \\frac{dy}{dt} = v_0$ \u3068\u3044\u3046\u521d\u671f\u6761\u4ef6\u3092\u8ab2\u3057\u3066\u7a4d\u5206\u5b9a\u6570\u3092\u6c7a\u3081\u308b\u4f8b\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[4]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u76f4\u524d\u306e\u89e3 % \u306b\u5bfe\u3057\u3066\u521d\u671f\u6761\u4ef6\u3092 ic2() \u3067\u8ab2\u3057\u307e\u3059\u3002*\/<\/span>\r\n<span class=\"nf\">ic2<\/span><span class=\"p\">(<\/span><span class=\"nv\">%<\/span>, <span class=\"nv\">t<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>, <span class=\"nv\">y<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>, <span class=\"o\">'<\/span><span class=\"nf\">diff<\/span><span class=\"p\">(<\/span><span class=\"nv\">y<\/span>, <span class=\"nv\">t<\/span><span class=\"p\">)<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">v0<\/span><span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u306e\u89e3\u306f\u5206\u6bcd\u306b $\\beta$ \u304c\u3042\u308a\uff0c\u5358\u7d14\u306b $\\beta = 0$ \u306b\u3059\u308b\u3068\u5927\u5909\u306a\u3053\u3068\u306b\u306a\u3063\u3066\u3057\u307e\u3044\u305d\u3046\u3067\u3059\u3002<\/p>\n<p>\u305d\u3053\u3067\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u6975\u9650\u3092\u3068\u3063\u3066\u307f\u307e\u3059\u3002<\/p>\n<p>$$\\lim_{\\beta \\rightarrow 0} y$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[5]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* 3. *\/<\/span>\r\n<span class=\"cm\">\/* \u76f4\u524d\u306e\u89e3\u306e beta -&gt; 0 \u306e\u6975\u9650\u3092\u3068\u308a\u307e\u3059\u3002*\/<\/span>\r\n<span class=\"nf\">limit<\/span><span class=\"p\">(<\/span><span class=\"nv\">%<\/span>, <span class=\"nv\">beta<\/span>, <span class=\"mi\">0<\/span><span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[6]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u524d\u554f 1. \u306e\u7b54\u3048\u306b\u4e00\u81f4\u3059\u308b\u3088\u3046\u306b\u5c55\u958b\u3057\u307e\u3059\u3002*\/<\/span>\r\n<span class=\"nf\">expand<\/span><span class=\"p\">(<\/span><span class=\"nv\">%<\/span><span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3\u6cd5-rk()\">\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3\u6cd5 <code>rk()<\/code><\/h3>\n<p>\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u304c\u89e3\u6790\u7684\u306b\u89e3\u3051\u306a\u3044\u3068\u304d\u306f\uff0c\u6570\u5024\u7684\u89e3\u6cd5\u306b\u3088\u3063\u3066\u8fd1\u4f3c\u5024\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002Maxima \u306b\u306f\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5\u306b\u3088\u3063\u3066\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u304f\u95a2\u6570 <code>rk()<\/code> \u304c\u3042\u3089\u304b\u3058\u3081\u7d44\u307f\u8fbc\u307e\u308c\u3066\u3044\u307e\u3059\u3002\u4f7f\u3044\u65b9\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n<h4 id=\"1\u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\">1\u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f<\/h4>\n<p>1\u968e\u306e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f<br \/>\n$$ \\frac{dx}{dt} = f(x, t)$$<br \/>\n\u3092\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5\u3067\u89e3\u304f\u4f8b\u3067\u3059\u3002<\/p>\n<p>\u521d\u671f\u6761\u4ef6\u3092 $t=t_0$ \u3067 $x(t_0) = x_0$ \u3068\u3057\uff0c$t=t_0$ \u304b\u3089 $t = t_1$ \u307e\u3067\u3092 $N$ \u5206\u5272\u3057\uff0c\u523b\u307f\u5e45 $\\displaystyle h = \\frac{t_1 &#8211; t_0}{N}$ \u3067 $x$ \u306b\u3064\u3044\u3066\u89e3\u304f\u5834\u5408\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3057\u307e\u3059\u3002<\/p>\n<p><code>rk(f(x,t), x, x0, [t, t0, t1, h])<\/code><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u4ee5\u4e0b\u3067\u306f\uff0c\u7c21\u5358\u306a\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u65b9\u7a0b\u5f0f<br \/>\n$$ \\frac{dx}{dt} = (1-x)\\,x$$<br \/>\n\u3092\uff0c\u521d\u671f\u6761\u4ef6 $t_0 = 0$ \u3067 $x_0 = x(t_0) = 0.1$\uff0c$t = t_0 = 0$ \u304b\u3089 $t_1 = 10$ \u307e\u3067\u3092 $ N = 100$ \u5206\u5272\u3057\u3066\u89e3\u304d\u307e\u3059\u3002<\/p>\n<p>Maxima \u306e <code>rk()<\/code> \u306f\u30b7\u30f3\u30d7\u30eb\u306a4\u6b21\u306e\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5\u3067\u3059\u304b\u3089\uff0c\u304d\u3056\u307f\u5e45 <code>h<\/code> \u306e\u53d6\u308a\u65b9\u304c\u8aa4\u5dee\u306b\u76f4\u7d50\u3057\u307e\u3059\u3002\u6570\u5024\u8a08\u7b97\u306e\u8aa4\u5dee\u306b\u3064\u3044\u3066\u306f\uff0c<code>h<\/code> \u3092\u5909\u3048\u3066\u8a08\u7b97\u3057\u3066\u307f\u3066\u7cbe\u5ea6\u3092\u78ba\u304b\u3081\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[7]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u53f3\u8fba *\/<\/span>\r\n<span class=\"nf\">f<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">t<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"p\">(<\/span>1<span class=\"o\">-<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span><span class=\"o\">*<\/span><span class=\"nv\">x<\/span>$ \r\n<span class=\"cm\">\/* t \u306e\u521d\u671f\u5024 *\/<\/span>\r\n<span class=\"nv\">t0<\/span><span class=\"o\">:<\/span> 0$ \r\n<span class=\"cm\">\/* x \u306e\u521d\u671f\u5024 *\/<\/span>\r\n<span class=\"nv\">x0<\/span><span class=\"o\">:<\/span> 0<span class=\"o\">.<\/span>1$\r\n<span class=\"cm\">\/* t \u306e\u7d42\u4e86\u5024 *\/<\/span>\r\n<span class=\"nv\">t1<\/span><span class=\"o\">:<\/span> 10$\r\n<span class=\"cm\">\/* \u5206\u5272\u6570 *\/<\/span>\r\n<span class=\"nv\">N<\/span><span class=\"o\">:<\/span> 100$\r\n<span class=\"cm\">\/* \u523b\u307f\u5e45 h \u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3057\u3066\u8a08\u7b97\u3055\u308c\u308b\u3002*\/<\/span>\r\n<span class=\"nv\">h<\/span><span class=\"o\">:<\/span> <span class=\"nf\">float<\/span><span class=\"p\">((<\/span><span class=\"nv\">t1<\/span> <span class=\"o\">-<\/span> <span class=\"nv\">t0<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"nv\">N<\/span><span class=\"p\">)<\/span>$ \r\n\r\n<span class=\"nv\">rkdat<\/span><span class=\"o\">:<\/span> <span class=\"nf\">rk<\/span><span class=\"p\">(<\/span><span class=\"nf\">f<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">t<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">x<\/span>, <span class=\"nv\">x0<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">t<\/span>, <span class=\"nv\">t0<\/span>, <span class=\"nv\">t1<\/span>, <span class=\"nv\">h<\/span><span class=\"p\">])<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5\u306b\u3088\u308b\u6570\u5024\u89e3\u306f\uff0c\u30ea\u30b9\u30c8 <code>rkdat<\/code> \u306b\u4ee3\u5165\u3057\u3066\u3044\u307e\u3059\u3002\u30ea\u30b9\u30c8 <code>rkdat<\/code> \u306e\u300c\u9577\u3055\u300d\uff08\u9805\u6570\uff09\u306f $N+1$ \u500b\u3067\u3059\u3002<\/p>\n<p>\u30ea\u30b9\u30c8 <code>rkdat<\/code> \u306e\u6700\u521d\u306e\u9805 <code>rkdat[1]<\/code> \u3092\u8868\u793a\u3055\u305b\u308b\u3068\uff0c$[t_0, x_0]$\uff0c\u6700\u5f8c\u306e\u9805 <code>rkdat[length(rkdat)]<\/code> \u306e\u5024\u306f $[t_1, x(t_1)]$ \u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[8]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">length<\/span><span class=\"p\">(<\/span><span class=\"nv\">rkdat<\/span><span class=\"p\">)<\/span>;\r\n<span class=\"nv\">rkdat<\/span><span class=\"p\">[<\/span>1<span class=\"p\">]<\/span>;\r\n<span class=\"nv\">rkdat<\/span><span class=\"p\">[<\/span><span class=\"nf\">length<\/span><span class=\"p\">(<\/span><span class=\"nv\">rkdat<\/span><span class=\"p\">)]<\/span>;\r\n<span class=\"nv\">rkdat<\/span><span class=\"p\">[<\/span><span class=\"nf\">length<\/span><span class=\"p\">(<\/span><span class=\"nv\">rkdat<\/span><span class=\"p\">)][<\/span>2<span class=\"p\">]<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[8]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{18}$}101\\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[8]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{19}$}\\left[ 0.0 , 0.1 \\right] \\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[8]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{20}$}\\left[ 10.0 , 0.9995915652218679 \\right] \\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[8]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{21}$}0.9995915652218679\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u523b\u307f\u5e45\u3092\u5909\u66f4\u3059\u308b\u3068\u6570\u5024\u89e3\u306e\u7cbe\u5ea6\u304c\u5909\u308f\u308a\u307e\u3059\u3002\u5ff5\u306e\u305f\u3081\uff0c$N$ \u3092\u5909\u66f4\u3057\u3066\u6570\u5024\u89e3\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[9]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* N \u306e\u5024\u3092\u5909\u3048\u3066\u6570\u5024\u89e3 x(t1) \u3092\u8868\u793a *\/<\/span>\r\n<span class=\"k\">for<\/span> <span class=\"nv\">N<\/span> <span class=\"nv\">in<\/span> <span class=\"p\">[<\/span><span class=\"mi\">100<\/span>, <span class=\"mi\">200<\/span>, <span class=\"mi\">400<\/span>, 800<span class=\"p\">]<\/span> <span class=\"k\">do<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nv\">h<\/span><span class=\"o\">:<\/span> <span class=\"nf\">float<\/span><span class=\"p\">((<\/span><span class=\"nv\">t1<\/span> <span class=\"o\">-<\/span> <span class=\"nv\">t0<\/span><span class=\"p\">)<\/span> <span class=\"o\">*<\/span> 1<span class=\"o\">.<\/span>0<span class=\"o\">\/<\/span><span class=\"nv\">N<\/span><span class=\"p\">)<\/span>,\r\n  <span class=\"nv\">rkdat<\/span><span class=\"o\">:<\/span> <span class=\"nf\">rk<\/span><span class=\"p\">(<\/span><span class=\"nf\">f<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">t<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">x<\/span>, <span class=\"nv\">x0<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">t<\/span>, <span class=\"nv\">t0<\/span>, <span class=\"nv\">t1<\/span>, <span class=\"nv\">h<\/span><span class=\"p\">])<\/span>,\r\n  <span class=\"nf\">print<\/span><span class=\"p\">(<\/span><span class=\"s\">\"N =\"<\/span>, <span class=\"nv\">N<\/span>, <span class=\"s\">\" x(t1) = \"<\/span>, <span class=\"nv\">rkdat<\/span><span class=\"p\">[<\/span><span class=\"nf\">length<\/span><span class=\"p\">(<\/span><span class=\"nv\">rkdat<\/span><span class=\"p\">)][<\/span>2<span class=\"p\">])<\/span>\r\n<span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_latex output_subarea \">N = \\(100\\) x(t1) = \\(0.9995915652218679\\)<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_latex output_subarea \">N = \\(200\\) x(t1) = \\(0.9995915673786502\\)<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_latex output_subarea \">N = \\(400\\) x(t1) = \\(0.9995915675088635\\)<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_latex output_subarea \">N = \\(800\\) x(t1) = \\(0.9995915675168631\\)<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u7d50\u679c\u3092\u898b\u6bd4\u3079\u305f\u9650\u308a\u3067\u306f\uff0c\u6570\u5024\u89e3\u306f $N=400$ \u3068\u3057\u305f\u5834\u5408\u306b<br \/>\n$$ x(t_1) = 0.9995915675&#8230;$$ \u3042\u305f\u308a\u307e\u3067\u306e\u7cbe\u5ea6\u304c\u3042\u308a\u305d\u3046\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5\u306b\u3088\u308b\u6570\u5024\u89e3\u306f\uff0c\u30ea\u30b9\u30c8 <code>rkdat<\/code> \u306b\u4ee3\u5165\u3055\u308c\u307e\u3059\u3002<br \/>\n\u3053\u308c\u3092\u30b0\u30e9\u30d5\u306b\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[10]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">plot2d<\/span><span class=\"p\">([<\/span><span class=\"nv\">discrete<\/span>, <span class=\"nv\">rkdat<\/span><span class=\"p\">])<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-4599\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxcon201.svg\" alt=\"\" width=\"640\" height=\"512\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"2\u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\">2\u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f<\/h4>\n<p>\u6b21\u306e\u3088\u3046\u306a2\u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5\u3067\u89e3\u304f\u3002<\/p>\n<p>$$ \\frac{d^2 x}{dt^2 } = f\\left(x, \\frac{dx}{dt}, t\\right)$$<\/p>\n<p>\u3053\u306e\u5834\u5408\u306b\u306f\uff0c $\\displaystyle v \\equiv \\frac{dx}{dt}$ \u3068\u304a\u3051\u3070\uff0c\u6b21\u306e\u3088\u3046\u306a\u9023\u7acb1\u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u5f62\u306b\u5e30\u7740\u3067\u304d\u308b\u3002<br \/>\n\\begin{eqnarray}<br \/>\n\\frac{dx}{dt} &amp;=&amp; F_1(x, v, t) = v \\\\<br \/>\n\\frac{dv}{dt} &amp;=&amp; F_2(x, v, t) = f(x, v, t)<br \/>\n\\end{eqnarray}<\/p>\n<p>\u521d\u671f\u6761\u4ef6\u3092 $t=t_0$ \u3067 $x(t_0) = x_0, v(t_0) = v_0$ \u3068\u3057\uff0c$t=t_0$ \u304b\u3089 $t = t_1$ \u307e\u3067\u3092 $N$ \u5206\u5272\u3057\uff0c\u523b\u307f\u5e45 $\\displaystyle h = \\frac{t_1 &#8211; t_0}{N}$ \u3067 $x, v$ \u306b\u3064\u3044\u3066\u89e3\u304f\u5834\u5408\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3057\u307e\u3059\u3002<\/p>\n<p><code>rk([F1(x,v,t), F2(x,v,t)], [x, v], [x0, v0], [t, t0, t1, h])<\/code><\/p>\n<p>\u4ee5\u4e0b\u3067\u306f\u4f8b\u3068\u3057\u3066\uff0c\u7c21\u5358\u306a\u6e1b\u8870\uff0b\u5f37\u5236\u632f\u52d5\u306e\u65b9\u7a0b\u5f0f<\/p>\n<p>$$ \\frac{d^2 x}{dt^2} = -x &#8211; a \\frac{dx}{dt} + b \\cos(t) $$<\/p>\n<p>\u3092\uff0c<\/p>\n<ul>\n<li>$a , b $ \u306b\u3044\u308d\u3044\u308d\u306a\u5024\u3092\u5165\u308c\u3066<\/li>\n<li>\u521d\u671f\u6761\u4ef6 $t_0 = 0$ \u3067 $x_0 = x(t_0) = 3, v_0 = v(t_0) = 0$\uff0c<\/li>\n<li>$t = t_0 = 0$ \u304b\u3089 $t_1 = 20$ \u307e\u3067\u3092 $ N $ \u5206\u5272<\/li>\n<\/ul>\n<p>\u3057\u3066\u89e3\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[12]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">F1<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">v<\/span>, <span class=\"nv\">t<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">v<\/span>$\r\n<span class=\"nf\">F2<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">v<\/span>, <span class=\"nv\">t<\/span>, <span class=\"nv\">a<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"o\">-<\/span><span class=\"nv\">x<\/span> <span class=\"o\">-<\/span> <span class=\"nv\">a<\/span><span class=\"o\">*<\/span><span class=\"nv\">v<\/span> <span class=\"o\">+<\/span> <span class=\"nv\">b<\/span><span class=\"o\">*<\/span><span class=\"nf\">cos<\/span><span class=\"p\">(<\/span><span class=\"nv\">t<\/span><span class=\"p\">)<\/span>$\r\n<span class=\"nv\">t0<\/span><span class=\"o\">:<\/span> <span class=\"mi\">0<\/span> $\r\n<span class=\"nv\">x0<\/span><span class=\"o\">:<\/span> <span class=\"mi\">3<\/span> $\r\n<span class=\"nv\">v0<\/span><span class=\"o\">:<\/span> <span class=\"mi\">0<\/span> $\r\n<span class=\"cm\">\/* t1: 20 $ *\/<\/span>\r\n<span class=\"nv\">t1<\/span><span class=\"o\">:<\/span> 20$\r\n\r\n<span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">true<\/span>,<span class=\"s\">\"\u3000N        h          x(t1)~%\"<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"k\">for<\/span> <span class=\"nv\">N<\/span> <span class=\"nv\">in<\/span> <span class=\"p\">[<\/span><span class=\"mi\">200<\/span>, <span class=\"mi\">500<\/span>, <span class=\"mi\">2000<\/span>, 5000<span class=\"p\">]<\/span> <span class=\"k\">do<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nv\">h<\/span><span class=\"o\">:<\/span> <span class=\"nf\">float<\/span><span class=\"p\">((<\/span><span class=\"nv\">t1<\/span> <span class=\"o\">-<\/span> <span class=\"nv\">t0<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"nv\">N<\/span><span class=\"p\">)<\/span>, \r\n  <span class=\"nv\">dat<\/span><span class=\"o\">:<\/span> <span class=\"nf\">rk<\/span><span class=\"p\">([<\/span><span class=\"nf\">F1<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>,<span class=\"nv\">v<\/span>,<span class=\"nv\">t<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">F2<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>,<span class=\"nv\">v<\/span>,<span class=\"nv\">t<\/span>,<span class=\"mi\">0<\/span>,<span class=\"mi\">0<\/span><span class=\"p\">)]<\/span>, \r\n          <span class=\"p\">[<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">v<\/span><span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">x0<\/span>, <span class=\"nv\">v0<\/span><span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">t<\/span>, <span class=\"nv\">t0<\/span>, <span class=\"nv\">t1<\/span>, <span class=\"nv\">h<\/span><span class=\"p\">])<\/span>,\r\n  <span class=\"cm\">\/* \u66f8\u5f0f\u6307\u5b9a\u306e printf()  *\/<\/span>\r\n  <span class=\"cm\">\/* ~5d \u306f\u6574\u65705\u6841\uff0c~10,5f \u306f\u6d6e\u52d5\u5c0f\u6570\u70b9\u657010\u6841\u3067\u5c0f\u6570\u70b9\u4ee5\u4e0b5\u6841 *\/<\/span>\r\n  <span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">true<\/span>, <span class=\"s\">\"~5d ~10,5f   ~12,10f~%\"<\/span>, \r\n                <span class=\"nv\">N<\/span>,  <span class=\"nv\">h<\/span>,       <span class=\"nv\">dat<\/span><span class=\"p\">[<\/span><span class=\"nf\">length<\/span><span class=\"p\">(<\/span><span class=\"nv\">dat<\/span><span class=\"p\">)][<\/span>2<span class=\"p\">])<\/span>\r\n<span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>\u3000N        h          x(t1)\r\n  200    0.10000   1.2242899713\r\n  500    0.04000   1.2242473359\r\n 2000    0.01000   1.2242461900\r\n 5000    0.00400   1.2242461856\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u4e0a\u8a18\u306e\u7d50\u679c\u304b\u3089\uff0c\u3060\u3044\u305f\u3044 $h = 0.01$ \u306e\u523b\u307f\u5e45\u3067\u5c0f\u6570\u70b9\u4ee5\u4e0b8\u6841\u7a0b\u5ea6\u306e\u7cbe\u5ea6\u304c\u3042\u308b\u3068\u63a8\u6e2c\u3055\u308c\u307e\u3059\u3002\u4ee5\u4e0b\u3067\u306f\uff0c\u3053\u306e\u5024\u3067\u8a08\u7b97\u3092\u7d9a\u3051\u307e\u3059\u3002<\/p>\n<p>$a = 0, b = 0$ \u306e\u5834\u5408\u306e\u6570\u5024\u89e3\u3092 <code>dataa00b00<\/code>\uff0c$a = 0.5, b = 0.2$ \u306e\u5834\u5408\u306e\u6570\u5024\u89e3\u3092 <code>data05b02<\/code> \u306b\u4ee3\u5165\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[13]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">h<\/span><span class=\"o\">:<\/span> 0<span class=\"o\">.<\/span>01$\r\n<span class=\"nv\">data00b00<\/span><span class=\"o\">:<\/span> \r\n  <span class=\"nf\">rk<\/span><span class=\"p\">([<\/span><span class=\"nf\">F1<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>,<span class=\"nv\">v<\/span>,<span class=\"nv\">t<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">F2<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>,<span class=\"nv\">v<\/span>,<span class=\"nv\">t<\/span>,<span class=\"mi\">0<\/span>,<span class=\"mi\">0<\/span><span class=\"p\">)]<\/span>, \r\n     <span class=\"p\">[<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">v<\/span><span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">x0<\/span>, <span class=\"nv\">v0<\/span><span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">t<\/span>, <span class=\"nv\">t0<\/span>, <span class=\"nv\">t1<\/span>, <span class=\"nv\">h<\/span><span class=\"p\">])<\/span>$\r\n<span class=\"nv\">data05b02<\/span><span class=\"o\">:<\/span> \r\n  <span class=\"nf\">rk<\/span><span class=\"p\">([<\/span><span class=\"nf\">F1<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>,<span class=\"nv\">v<\/span>,<span class=\"nv\">t<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">F2<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>,<span class=\"nv\">v<\/span>,<span class=\"nv\">t<\/span>,<span class=\"mf\">0.5<\/span>,<span class=\"mf\">0.2<\/span><span class=\"p\">)]<\/span>, \r\n     <span class=\"p\">[<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">v<\/span><span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">x0<\/span>, <span class=\"nv\">v0<\/span><span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">t<\/span>, <span class=\"nv\">t0<\/span>, <span class=\"nv\">t1<\/span>, <span class=\"nv\">h<\/span><span class=\"p\">])<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u4ee5\u4e0b\u306e\u4f8b\u304b\u3089\u308f\u304b\u308b\u3088\u3046\u306b\uff0c\u3053\u308c\u3089\u306e\u30ea\u30b9\u30c8\u306f1\u5217\u76ee\u304c $t$, 2\u5217\u76ee\u304c $x$, 3\u5217\u76ee\u304c $v$ \u306e\u5024\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[14]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">data00b00<\/span><span class=\"p\">[<\/span>1<span class=\"p\">]<\/span>;\r\n<span class=\"nv\">data00b00<\/span><span class=\"p\">[<\/span><span class=\"nf\">length<\/span><span class=\"p\">(<\/span><span class=\"nv\">data00b00<\/span><span class=\"p\">)]<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[14]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{36}$}\\left[ 0.0 , 3.0 , 0.0 \\right] \\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[14]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{37}$}\\left[ 20.0 , 1.224246189987741 , -2.738835750104511 \\right] \\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>1\u5217\u76ee\u306e\u30c7\u30fc\u30bf\u3092\u6a2a\u8ef8\uff0c2\u5217\u76ee\u306e\u30c7\u30fc\u30bf\u3092\u7e26\u8ef8\u306b\u3068\u3063\u3066\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u4f8b\u3067\u3059\u3002<\/p>\n<p><code>makelist([c[1],c[2]], c, data00b00)<\/code> \u304c\u30ad\u30e2\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[15]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">plot2d<\/span><span class=\"p\">([<\/span><span class=\"nv\">discrete<\/span>, <span class=\"nf\">makelist<\/span><span class=\"p\">([<\/span><span class=\"nv\">c<\/span><span class=\"p\">[<\/span>1<span class=\"p\">]<\/span>,<span class=\"nv\">c<\/span><span class=\"p\">[<\/span>2<span class=\"p\">]]<\/span>, <span class=\"nv\">c<\/span>, <span class=\"nv\">data00b00<\/span><span class=\"p\">)])<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-4600\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxcon202.svg\" alt=\"\" width=\"640\" height=\"512\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>2\u3064\u306e\u30c7\u30fc\u30bf\u306e\u30b0\u30e9\u30d5\u3092\u91cd\u306d\u3066\u8868\u793a\u3059\u308b\u4f8b\u3067\u3059\u3002\u51e1\u4f8b\u3084\u30b0\u30ea\u30c3\u30c9\u3082\u8a2d\u5b9a\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[17]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u51e1\u4f8b\u304c\u66f2\u7dda\u3068\u304b\u3076\u3089\u306a\u3044\u3088\u3046\u306b y \u306e\u8868\u793a\u7bc4\u56f2\u3092\u8a2d\u5b9a *\/<\/span>\r\n<span class=\"nf\">plot2d<\/span><span class=\"p\">([[<\/span><span class=\"nv\">discrete<\/span>, <span class=\"nf\">makelist<\/span><span class=\"p\">([<\/span><span class=\"nv\">c<\/span><span class=\"p\">[<\/span>1<span class=\"p\">]<\/span>,<span class=\"nv\">c<\/span><span class=\"p\">[<\/span>2<span class=\"p\">]]<\/span>, <span class=\"nv\">c<\/span>, <span class=\"nv\">data00b00<\/span><span class=\"p\">)]<\/span>,  \r\n        <span class=\"p\">[<\/span><span class=\"nv\">discrete<\/span>, <span class=\"nf\">makelist<\/span><span class=\"p\">([<\/span><span class=\"nv\">c<\/span><span class=\"p\">[<\/span>1<span class=\"p\">]<\/span>,<span class=\"nv\">c<\/span><span class=\"p\">[<\/span>2<span class=\"p\">]]<\/span>, <span class=\"nv\">c<\/span>, <span class=\"nv\">data05b02<\/span><span class=\"p\">)]]<\/span>, \r\n       <span class=\"nv\">grid2d<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">y<\/span>, <span class=\"o\">-<\/span><span class=\"mf\">3.2<\/span>, 3<span class=\"o\">.<\/span>9<span class=\"p\">]<\/span>,\r\n       <span class=\"p\">[<\/span><span class=\"nv\">legend<\/span>, <span class=\"s\">\"a = 0 ,  b = 0\"<\/span>, \r\n                <span class=\"s\">\"a = 0.5, b = 0.2\"<\/span><span class=\"p\">]<\/span>\r\n<span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-4601\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxcon203.svg\" alt=\"\" width=\"640\" height=\"512\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u7df4\u7fd2-2-2\">\u7df4\u7fd2 2-2<\/h4>\n<p>$ a = 0.5, b = 0$ \u306e\u6e1b\u8870\u632f\u52d5\u306e\u5834\u5408\u306e\u6570\u5024\u89e3\u3092\u540c\u69d8\u306b\u3057\u3066\u3082\u3068\u3081\uff0c<br \/>\n\u4e0a\u8a18\u306e $a = 0.5, b = 0.2$ \u306e\u6e1b\u8870\uff0b\u5f37\u5236\u632f\u52d5\u306e\u89e3\u3068\u6bd4\u8f03\u305b\u3088\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[\u00a0]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u53c2\u8003\uff1a\u6e1b\u8870\uff0b\u5f37\u5236\u632f\u52d5\u306e\u89e3\u6790\u89e3\">\u53c2\u8003\uff1a\u6e1b\u8870\uff0b\u5f37\u5236\u632f\u52d5\u306e\u89e3\u6790\u89e3<\/h4>\n<p>\u5b9f\u306f Maxima \u3067\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u6e1b\u8870\uff0b\u5f37\u5236\u632f\u52d5\u306e\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092 <code>ode2()<\/code> \u306b\u3088\u3063\u3066\u89e3\u6790\u7684\u306b\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u4ee5\u4e0b\u3067\u306f\uff0c<br \/>\n$$ \\frac{d^2 x}{dt^2} = -x &#8211; a \\frac{dx}{dt} + b \\cos(t) $$<br \/>\n\u3092\uff0c$a = 0.5, b = 0.2$ \u306e\u5834\u5408\u306b\u89e3\u6790\u7684\u306b\u89e3\u304f\u4f8b\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n<p>\u89e3\u304f\u3079\u304d\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u8a18\u8ff0\u4f8b\u3067\u3059\u3002\u5fae\u5206 <code>diff()<\/code> \u306e\u524d\u306b <code>'<\/code> \u3092\u3064\u3051\u3066\u66f8\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[19]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">a<\/span><span class=\"o\">:<\/span> 5<span class=\"o\">\/<\/span>10$\r\n<span class=\"nv\">b<\/span><span class=\"o\">:<\/span> 2<span class=\"o\">\/<\/span>10$\r\n<span class=\"nv\">eq<\/span><span class=\"o\">:<\/span> <span class=\"o\">'<\/span><span class=\"nf\">diff<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">t<\/span>, <span class=\"mi\">2<\/span><span class=\"p\">)<\/span> <span class=\"o\">=<\/span> <span class=\"o\">-<\/span> <span class=\"nv\">x<\/span> <span class=\"o\">-<\/span> <span class=\"nv\">a<\/span> <span class=\"o\">*<\/span> <span class=\"o\">'<\/span><span class=\"nf\">diff<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>,<span class=\"nv\">t<\/span><span class=\"p\">)<\/span> <span class=\"o\">+<\/span> <span class=\"nv\">b<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">cos<\/span><span class=\"p\">(<\/span><span class=\"nv\">t<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[19]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{44}$}\\frac{d^2}{d\\,t^2}\\,x=-\\frac{\\frac{d}{d\\,t}\\,x}{2}-x+\\frac{\\cos t}{5}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[20]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">ode2<\/span><span class=\"p\">(<\/span><span class=\"nv\">eq<\/span>, <span class=\"nv\">x<\/span>, <span class=\"nv\">t<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[20]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{45}$}x=e^ {- \\frac{t}{4} }\\,\\left({\\it \\%k}_{1}\\,\\sin \\left(\\frac{\\sqrt{15}\\,t}{4}\\right)+{\\it \\%k}_{2}\\,\\cos \\left(\\frac{\\sqrt{15}\\,t}{4}\\right)\\right)+\\frac{2\\,\\sin t}{5}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u4e0a\u8a18\u306e\u89e3\u306f\uff0c2\u3064\u306e\u7a4d\u5206\u5b9a\u6570 $\\%k_1, \\%k_2$ \u3092\u542b\u3080\u4e00\u822c\u89e3\u3067\u3059\u3002<\/p>\n<p>2\u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u521d\u671f\u6761\u4ef6\u306f <code>ic2()<\/code> \u95a2\u6570\u3067\u4e0e\u3048\u307e\u3059\u3002\u4ee5\u4e0b\u3067\u306f\uff0c\u521d\u671f\u6761\u4ef6\u3068\u3057\u3066 $t = 0$ \u3067 $x = 3, \\frac{dx}{dt} = 0$ \u3092\u8a2d\u5b9a\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[21]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">ic2<\/span><span class=\"p\">(<\/span><span class=\"nv\">%<\/span>, <span class=\"nv\">t<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>, <span class=\"nv\">x<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">3<\/span>, <span class=\"o\">'<\/span><span class=\"nf\">diff<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">t<\/span><span class=\"p\">)<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[21]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{46}$}x=e^ {- \\frac{t}{4} }\\,\\left(\\frac{7\\,\\sin \\left(\\frac{\\sqrt{15}\\,t}{4}\\right)}{5\\,\\sqrt{15}}+3\\,\\cos \\left(\\frac{\\sqrt{15}\\,t}{4}\\right)\\right)+\\frac{2\\,\\sin t}{5}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u306e\u89e3\u3092\u95a2\u6570 <code>x(t)<\/code> \u3068\u3057\u3066\u5b9a\u7fa9\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[22]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">define<\/span><span class=\"p\">(<\/span><span class=\"nf\">x<\/span><span class=\"p\">(<\/span><span class=\"nv\">t<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">rhs<\/span><span class=\"p\">(<\/span><span class=\"nv\">%<\/span><span class=\"p\">))<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5 <code>rk()<\/code> \u3067\u6c42\u3081\u305f\u6570\u5024\u89e3\u3068\u4e00\u7dd2\u306b\u56f3\u793a\u3057\u307e\u3059\u3002\u6570\u5024\u89e3\u306f2001\u500b\u3068\u591a\u3044\u306e\u3067\uff0c\u9593\u5f15\u3044\u305f\u30ea\u30b9\u30c8 <code>rkdat<\/code> \u3092\u4f5c\u308a\uff0c\u63cf\u753b\u30b9\u30bf\u30a4\u30eb\u3092 <code>points<\/code> \u306b\u3057\u3066\u30b0\u30e9\u30d5\u306b\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[23]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">length<\/span><span class=\"p\">(<\/span><span class=\"nv\">data05b02<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[23]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{48}$}2001\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[24]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u30ea\u30b9\u30c8\u3092 100 \u304a\u304d\u306b\u9593\u5f15\u304f\u4f8b *\/<\/span>\r\n<span class=\"nv\">rkdat<\/span><span class=\"o\">:<\/span> <span class=\"nf\">makelist<\/span><span class=\"p\">(<\/span><span class=\"nv\">data05b02<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]<\/span>, <span class=\"nv\">i<\/span>, <span class=\"mi\">1<\/span>, <span class=\"nf\">length<\/span><span class=\"p\">(<\/span><span class=\"nv\">data05b02<\/span><span class=\"p\">)<\/span>, <span class=\"mi\">100<\/span><span class=\"p\">)<\/span>$\r\n<span class=\"nf\">length<\/span><span class=\"p\">(<\/span><span class=\"nv\">rkdat<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[24]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{50}$}21\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[25]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* point_type \u306f bullet, box, triangle, plus, times, asterisk *\/<\/span>\r\n\r\n<span class=\"nf\">plot2d<\/span><span class=\"p\">([<\/span><span class=\"nf\">x<\/span><span class=\"p\">(<\/span><span class=\"nv\">t<\/span><span class=\"p\">)<\/span>,\r\n       <span class=\"p\">[<\/span><span class=\"nv\">discrete<\/span>, <span class=\"nf\">makelist<\/span><span class=\"p\">([<\/span><span class=\"nv\">c<\/span><span class=\"p\">[<\/span>1<span class=\"p\">]<\/span>,<span class=\"nv\">c<\/span><span class=\"p\">[<\/span>2<span class=\"p\">]]<\/span>, <span class=\"nv\">c<\/span>, <span class=\"nv\">rkdat<\/span><span class=\"p\">)]]<\/span>, \r\n       <span class=\"p\">[<\/span><span class=\"nv\">t<\/span>, <span class=\"mi\">0<\/span>, 20<span class=\"p\">]<\/span>, \r\n       <span class=\"nv\">grid2d<\/span>, \r\n       <span class=\"p\">[<\/span><span class=\"nv\">style<\/span>, <span class=\"nv\">lines<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">points<\/span>, 1<span class=\"p\">]]<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">point_type<\/span>, <span class=\"nv\">bullet<\/span><span class=\"p\">]<\/span>,\r\n       <span class=\"p\">[<\/span><span class=\"nv\">legend<\/span>, <span class=\"s\">\"\u89e3\u6790\u89e3\"<\/span>, <span class=\"s\">\"\u6570\u5024\u89e3\"<\/span><span class=\"p\">]<\/span>\r\n<span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-4602\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxcon204.svg\" alt=\"\" width=\"640\" height=\"512\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5ff5\u306e\u305f\u3081\u306b\uff0c$t=t_1$ \u3067\u306e\u6570\u5024\u89e3\u3068\u89e3\u6790\u89e3\u3092\u6bd4\u3079\u3066\u307f\u307e\u3059\u3002 \uff08\u5c0f\u6570\u70b9\u4ee5\u4e0b9\u6841\u7a0b\u5ea6\u306e\u7cbe\u5ea6\u304c\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3067\u3057\u3087\u3046\u304b\u3002\uff09<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[27]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">print<\/span><span class=\"p\">(<\/span><span class=\"nv\">data05b02<\/span><span class=\"p\">[<\/span><span class=\"nf\">length<\/span><span class=\"p\">(<\/span><span class=\"nv\">data05b02<\/span><span class=\"p\">)][<\/span>2<span class=\"p\">])<\/span>$\r\n<span class=\"nf\">print<\/span><span class=\"p\">(<\/span><span class=\"nf\">float<\/span><span class=\"p\">(<\/span><span class=\"nf\">x<\/span><span class=\"p\">(<\/span><span class=\"nv\">t1<\/span><span class=\"p\">)))<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_latex output_subarea \">\\(0.3839668594257015\\)<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_latex output_subarea \">\\(0.3839668593736918\\)<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Maxima \u3067\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3002\u89e3\u6790\u7684\u306b\uff0c\u3042\u308b\u3044\u306f\u6570\u5024\u7684\u306b\u3002<\/p><p><a class=\"more-link btn\" href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/%e5%8f%82%e8%80%83%ef%bc%9amaxima-%e7%b7%a8\/maxima-%e3%81%ab%e3%82%88%e3%82%8b%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/maxima-%e3%81%a6%e3%82%99%e5%b8%b8%e5%be%ae%e5%88%86%e6%96%b9%e7%a8%8b%e5%bc%8f\/\">\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"parent":4506,"menu_order":5,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-4598","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/4598","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/users\/33"}],"replies":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/comments?post=4598"}],"version-history":[{"count":7,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/4598\/revisions"}],"predecessor-version":[{"id":4662,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/4598\/revisions\/4662"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/4506"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=4598"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}