Data commit

Task/Runge-Kutta-method/Go/runge-kutta-method.go

@@ -0,0 +1,57 @@
+package main
+
+import (
+    "fmt"
+    "math"
+)
+
+type ypFunc func(t, y float64) float64
+type ypStepFunc func(t, y, dt float64) float64
+
+// newRKStep takes a function representing a differential equation
+// and returns a function that performs a single step of the forth-order
+// Runge-Kutta method.
+func newRK4Step(yp ypFunc) ypStepFunc {
+    return func(t, y, dt float64) float64 {
+        dy1 := dt * yp(t, y)
+        dy2 := dt * yp(t+dt/2, y+dy1/2)
+        dy3 := dt * yp(t+dt/2, y+dy2/2)
+        dy4 := dt * yp(t+dt, y+dy3)
+        return y + (dy1+2*(dy2+dy3)+dy4)/6
+    }
+}
+
+// example differential equation
+func yprime(t, y float64) float64 {
+    return t * math.Sqrt(y)
+}
+
+// exact solution of example
+func actual(t float64) float64 {
+    t = t*t + 4
+    return t * t / 16
+}
+
+func main() {
+    t0, tFinal := 0, 10 // task specifies times as integers,
+    dtPrint := 1        // and to print at whole numbers.
+    y0 := 1.            // initial y.
+    dtStep := .1        // step value.
+
+    t, y := float64(t0), y0
+    ypStep := newRK4Step(yprime)
+    for t1 := t0 + dtPrint; t1 <= tFinal; t1 += dtPrint {
+        printErr(t, y) // print intermediate result
+        for steps := int(float64(dtPrint)/dtStep + .5); steps > 1; steps-- {
+            y = ypStep(t, y, dtStep)
+            t += dtStep
+        }
+        y = ypStep(t, y, float64(t1)-t) // adjust step to integer time
+        t = float64(t1)
+    }
+    printErr(t, y) // print final result
+}
+
+func printErr(t, y float64) {
+    fmt.Printf("y(%.1f) = %f Error: %e\n", t, y, math.Abs(actual(t)-y))
+}