Data commit

Task/Runge-Kutta-method/Python/runge-kutta-method.py

@@ -0,0 +1,35 @@
+from math import sqrt
+
+def rk4(f, x0, y0, x1, n):
+    vx = [0] * (n + 1)
+    vy = [0] * (n + 1)
+    h = (x1 - x0) / float(n)
+    vx[0] = x = x0
+    vy[0] = y = y0
+    for i in range(1, n + 1):
+        k1 = h * f(x, y)
+        k2 = h * f(x + 0.5 * h, y + 0.5 * k1)
+        k3 = h * f(x + 0.5 * h, y + 0.5 * k2)
+        k4 = h * f(x + h, y + k3)
+        vx[i] = x = x0 + i * h
+        vy[i] = y = y + (k1 + k2 + k2 + k3 + k3 + k4) / 6
+    return vx, vy
+
+def f(x, y):
+    return x * sqrt(y)
+
+vx, vy = rk4(f, 0, 1, 10, 100)
+for x, y in list(zip(vx, vy))[::10]:
+    print("%4.1f %10.5f %+12.4e" % (x, y, y - (4 + x * x)**2 / 16))
+
+ 0.0    1.00000  +0.0000e+00
+ 1.0    1.56250  -1.4572e-07
+ 2.0    4.00000  -9.1948e-07
+ 3.0   10.56250  -2.9096e-06
+ 4.0   24.99999  -6.2349e-06
+ 5.0   52.56249  -1.0820e-05
+ 6.0   99.99998  -1.6595e-05
+ 7.0  175.56248  -2.3518e-05
+ 8.0  288.99997  -3.1565e-05
+ 9.0  451.56246  -4.0723e-05
+10.0  675.99995  -5.0983e-05