Data commit

Task/Euler-method/Maxima/euler-method.maxima

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+euler_method(f, y0, a, b, h):= block(
+  [t: a, y: y0, tg: [a], yg: [y0]],
+  unless t>=b do (
+    t: t + h,
+    y: y + f(t, y)*h,
+    tg: endcons(t, tg),
+    yg: endcons(y, yg)
+    ),
+  [tg, yg]
+  );
+
+/* initial temperature */
+T0: 100;
+
+/* environment of temperature */
+Tr: 20;
+
+/* the cooling constant */
+k: 0.07;
+
+/* end of integration */
+tmax: 100;
+
+/* analytical solution */
+Tref(t):= Tr + (T0 - Tr)*exp(-k*t);
+
+/* cooling rate */
+dT(t, T):= -k*(T-Tr);
+
+/* get numerical solution */
+h: 10;
+[tg, yg]: euler_method('dT, T0, 0, tmax,  h);
+
+/* plot analytical and numerical solution */
+plot2d([Tref, [discrete, tg, yg]], ['t, 0, tmax],
+  [legend, "analytical", concat("h = ", h)],
+  [xlabel, "t / seconds"],
+  [ylabel, "Temperature / C"]);