50 lines
1.1 KiB
Python
50 lines
1.1 KiB
Python
# Verfahren von Heun zur numerischen Lösung von Anfangswertaufgaben.
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#
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#def heun(xk,yk,h,ys):
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# xk1 = xk + h
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# yk1p = yk + h * ys(xk,yk)
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# yk1 = 0.5*(yk+yk1p+h*ys(xk1,yk1p))
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# return (xk1,yk1p)
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#
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#def run_heun(K,h,x0,y0,ys):
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# if not isinstance(ys,list): ys = [ys]
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# if not isinstance(y0,list): y0 = [y0]
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# xk = x0
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# yk = y0
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# xks = x0
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# yks = [ [v] for v in y0 ]
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#
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# for i in range(K):
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# for j in range(len(ys)):
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# xk,yk[j] = heun(xk,yk[j],h,ys[i])
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# xks.append(xk)
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# yks[j].append(yk[j])
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#
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def run_heun(K,h,x0,y0,ys):
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if not isinstance(y0,list): y0 = [y0]
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if not isinstance(ys,list): ys = [ys]
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xk = x0
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yk = y0
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xka = 0
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yka = [0]*len(yk)
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ykp = [0]*len(yk)
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xks = [x0]
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yks = [ [v] for v in y0 ]
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for i in range(K):
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xka = xk + h
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xks.append(xka)
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for j in range(len(ys)):
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yka[j] = yk[j] + h * ys[j](xk,*yk)
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for j in range(len(ys)):
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ykp[j] = 0.5*(yk[j] + yka[j] + h * ys[j](xka,*yka))
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yks[j].append(ykp[j])
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yk = ykp
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xk = xka
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return [xks] + yks
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