June 2018 Update

Task/Runge-Kutta-method/Nim/runge-kutta-method.nim

@@ -0,0 +1,26 @@
+import math
+
+proc fn(t, y: float): float =
+    result = t * math.sqrt(y)
+
+proc solution(t: float): float =
+    result = (t^2 + 4)^2 / 16
+
+proc rk(start, stop, step: float) =
+    let nsteps = int(round((stop - start) / step)) + 1
+    let delta = (stop - start) / float(nsteps - 1)
+    var cur_y = 1.0
+    for i in 0..(nsteps - 1):
+        let cur_t = start + delta * float(i)
+
+        if abs(cur_t - math.round(cur_t)) < 1e-5:
+            echo "y(", cur_t, ") = ", cur_y, ", error = ", solution(cur_t) - cur_y
+
+        let dy1 = step * fn(cur_t, cur_y)
+        let dy2 = step * fn(cur_t + 0.5 * step, cur_y + 0.5 * dy1)
+        let dy3 = step * fn(cur_t + 0.5 * step, cur_y + 0.5 * dy2)
+        let dy4 = step * fn(cur_t + step, cur_y + dy3)
+
+        cur_y += (dy1 + 2.0 * (dy2 + dy3) + dy4) / 6.0
+
+rk(start=0.0, stop=10.0, step=0.1)