Python中Runge-Kutta的方法

Method of Runge-Kutta in Python

我在python中编写了一个关于runge-kutta方法的代码，但每当程序实现任何微积分时，程序都需要微分方程。

这是我的代码：

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from math import *
import numpy as np

#Initial Values
n=input("Enter the number of equations n:")
n=int(n)
x=np.array([])
for i in range(0,n):
x0=input("Enter the initial value of x{}:".format(i))
x=np.append(x,[x0])
t=input("Enter the initial value of t:")
tf=input("Enter the final value of t:")
h=input("Enter the time interval h:")
m=int((tf-t)/float(h))

#Definition of differential equations
def f(t,x):
f=np.array([])
for i in range(0,n):
f0=input("Enter the equation f{}:".format(i))
f=np.append(f,[f0])
return f

a=1.0/6
for i in range(0,m):
k1=f(t,x)
k2=f(t+0.5*h,x+0.5*h*k1)
k3=f(t+0.5*h,x+0.5*h*k2)
k4=f(t+h,x+h*k3)
x=x+a*h*(k1+2*(k2+k3)+k4)
t=t+h

print t, x

使用等式dx / dt = x，x(0)= 1，xf = 1，h = 0.1的示例：

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Enter the number of equations n:1
Enter the initial value of x0:1
Enter the initial value of t:0
Enter the final value of t:1
Enter the time interval h:0.1
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
Enter the equation f0:x[0]
1.0 [ 2.71827974]

如果程序的微分方程计算全部，我该怎么办？

您必须将等式输入代码移出函数f(x,y)

要求在同一个块中输入方程式，就像要求所有其他输入一样。

因为它代表您的代码在每个时间间隔调用函数，因此将在每个时间间隔请求输入。