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Task/Runge-Kutta-method/JavaScript/runge-kutta-method.js

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+function rk4(y, x, dx, f) {
+    var k1 = dx * f(x, y),
+        k2 = dx * f(x + dx / 2.0,   +y + k1 / 2.0),
+        k3 = dx * f(x + dx / 2.0,   +y + k2 / 2.0),
+        k4 = dx * f(x + dx,         +y + k3);
+
+    return y + (k1 + 2.0 * k2 + 2.0 * k3 + k4) / 6.0;
+}
+
+function f(x, y) {
+    return x * Math.sqrt(y);
+}
+
+function actual(x) {
+    return (1/16) * (x*x+4)*(x*x+4);
+}
+
+var y = 1.0,
+    x = 0.0,
+    step = 0.1,
+    steps = 0,
+    maxSteps = 101,
+    sampleEveryN = 10;
+
+while (steps < maxSteps) {
+    if (steps%sampleEveryN === 0) {
+        console.log("y(" + x + ") =  \t" + y + "\t ± " + (actual(x) - y).toExponential());
+    }
+
+    y = rk4(y, x, step, f);
+
+    // using integer math for the step addition
+    // to prevent floating point errors as 0.2 + 0.1 != 0.3
+    x = ((x * 10) + (step * 10)) / 10;
+    steps += 1;
+}