Python中的Runge-Kutta方法

Question

我用python编写了关于runge方法的代码，但是每次当程序实现任何微积分时，程序都需要微分方程。

这是我的密码：

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

使用方程dx/dt=x，x(0)=1，xf=1，h=0.1：

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]

我该怎么做才能只输入一次微分方程来计算全部呢？

Answer 1

如果我不明白就纠正我。您是否试图获得用户手动输入的表达式，并将其视为函数？我找到了本题，它解释了如何使用渐近解析公式。您可以尝试使用同情修改程序。以这种方式，你应该能够一劳永逸地得到你的方程式。

编辑:如果你的问题只是“如何从输入得到整个公式一次.”您可以尝试使用raw_input()方法。还可以看一下这里

Answer 2

您必须将方程输入代码移出函数f(x,y)。

请将方程输入到与您要求的所有其他输入相同的块中。

当它处于状态时，您的代码将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。