36 lines
1.0 KiB
Python
36 lines
1.0 KiB
Python
from math import sqrt
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def rk4(f, x0, y0, x1, n):
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vx = [0]*(n + 1)
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vy = [0]*(n + 1)
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h = (x1 - x0)/n
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vx[0] = x = x0
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vy[0] = y = y0
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for i in range(1, n + 1):
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k1 = h*f(x, y)
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k2 = h*f(x + 0.5*h, y + 0.5*k1)
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k3 = h*f(x + 0.5*h, y + 0.5*k2)
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k4 = h*f(x + h, y + k3)
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vx[i] = x = x0 + i*h
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vy[i] = y = y + (k1 + k2 + k2 + k3 + k3 + k4)/6
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return vx, vy
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def f(x, y):
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return x*sqrt(y)
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vx, vy = rk4(f, 0, 1, 10, 100)
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for x, y in list(zip(vx, vy))[::10]:
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print(x, y, y - (4 + x*x)**2/16)
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0 1 0.0
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1.0 1.562499854278108 -1.4572189210859676e-07
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2.0 3.9999990805207997 -9.194792003341945e-07
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3.0 10.562497090437551 -2.9095624487496252e-06
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4.0 24.999993765090636 -6.234909363911356e-06
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5.0 52.562489180302585 -1.0819697415342944e-05
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6.0 99.99998340540358 -1.659459641700778e-05
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7.0 175.56247648227125 -2.3517728749311573e-05
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8.0 288.9999684347986 -3.156520142510999e-05
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9.0 451.56245927683966 -4.07231603389846e-05
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10.0 675.9999490167097 -5.098329029351589e-05
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