Python中的龙格-库塔方法

Question

我用python写了一个龙格-库塔方法的代码，但是每次当程序实现任何微积分时，程序都需要微分方程。

这是我的代码:

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的例子:

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所有的程序?

Answer 1

如果我没听懂请纠正我。您是否试图获得用户手动键入的表达式并将其视为函数?我发现了这个主题，它解释了如何使用sympy解析公式。您可以尝试使用sympy修改您的程序。用这种方法，你应该能够一次得到你的方程。

编辑:如果你的问题只是"如何获得整个公式一次从输入…"你可以尝试使用raw_input()方法。也看看这里:

Answer 2

您必须将公式输入代码移出函数f(x,y)

要求在同一块中输入方程式，因为您要求所有其他输入。

你的代码每隔一段时间就调用这个函数，所以每隔一段时间就会请求输入