Runge-Kutta method: Difference between revisions

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 y[t] -> 1/16*(4+t^2)^2 /. t -> Range[10]
 ->y[{1,2,3,4,5,6,7,8,9,10}]->{25/16, 4, 169/16, 25, 841/16, 100, 2809/16, 289, 7225/16, 676}</lang>
+=={{header|Maxima}}==
+<lang maxima>'diff(y,x) = x*sqrt(y);
+ode2(%, y, x);
+ic1(%, x=0, y=1);
+factor(solve(%, y)); /* [y=(x^2+4)^2/16] */
+rk4(f, x0, y0, x1, n) := block([h, x, y, vx, vy, k1, k2, k3, k4],
+   h: bfloat((x1 - x0)/(n - 1)),
+   x: x0,
+   y: y0,
+   vx: makelist(0, n + 1),
+   vy: makelist(0, n + 1),
+   vx[1]: x0,
+   vy[1]: y0,
+   for i from 1 thru n do (
+      k1: bfloat(h*f(x, y)),
+      k2: bfloat(h*f(x + h/2, y + k1/2)),
+      k3: bfloat(h*f(x + h/2, y + k2/2)),
+      k4: bfloat(h*f(x + h, y + k3)),
+      vy[i + 1]: y: y + (k1 + 2*k2 + 2*k3 + k4)/6,
+      vx[i + 1]: x: x + h
+   ),
+   [vx, vy]
+)$
+[x, y]: rk4(lambda([x, y], x*sqrt(y)), 0, 1, 10, 101)$
+plot2d([discrete, x, y])$
+s: map(lambda([x], (x^2 + 4)^2/16), x)$
+for i from 1 step 10 thru 101 do print(x[i], " ", y[i], " ", y[i] - s[i]);</lang>
 =={{header|Perl 6}}==
 {{works with|niecza|2012-04-3}}