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2016 Update

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This commit is contained in:
Tina Müller 2016-12-05 22:15:40 +01:00
parent 948b86eafa
commit dcf5d15da3
7965 changed files with 139854 additions and 31002 deletions
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44
Task/Runge-Kutta-method/Python/runge-kutta-method-2.py
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@ -1,35 +1,35 @@
from math import sqrt
def rk4(f, x0, y0, x1, n):
vx = [0]*(n + 1)
vy = [0]*(n + 1)
h = (x1 - x0)/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
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)
return x * sqrt(y)
vx, vy = rk4(f, 0, 1, 10, 100)
for x, y in list(zip(vx, vy))[::10]:
print(x, y, y - (4 + x*x)**2/16)
print("%4.1f %10.5f %+12.4e" % (x, y, y - (4 + x * x)**2 / 16))
0 1 0.0
1.0 1.562499854278108 -1.4572189210859676e-07
2.0 3.9999990805207997 -9.194792003341945e-07
3.0 10.562497090437551 -2.9095624487496252e-06
4.0 24.999993765090636 -6.234909363911356e-06
5.0 52.562489180302585 -1.0819697415342944e-05
6.0 99.99998340540358 -1.659459641700778e-05
7.0 175.56247648227125 -2.3517728749311573e-05
8.0 288.9999684347986 -3.156520142510999e-05
9.0 451.56245927683966 -4.07231603389846e-05
10.0 675.9999490167097 -5.098329029351589e-05
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