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Task/Runge-Kutta-method/Sidef/runge-kutta-method.sidef

@@ -0,0 +1,21 @@
+func runge_kutta(yp) {
+    func (t, y, δt) {
+        var a = (δt * yp(t, y));
+        var b = (δt * yp(t + δt/2, y + a/2));
+        var c = (δt * yp(t + δt/2, y + b/2));
+        var d = (δt * yp(t + δt, y + c));
+        (a + 2*(b + c) + d) / 6;
+    }
+}
+
+define δt = 0.1;
+var δy = runge_kutta(func(t, y) { t * y.sqrt });
+
+var(t, y) = (0, 1);
+loop {
+    t.is_int &&
+        printf("y(%2d) = %12f ± %e\n", t, y, abs(y - ((t**2 + 4)**2 / 16)));
+    t <= 10 || break;
+    y += δy(t, y, δt);
+    t += δt;
+}