Question

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：

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

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，我应该怎么做？

Answer 1

您必须将等式输入代码移出函数f(x,y)

要求在同一个区块中输入方程式，而不是要求所有其他输入。

现在你的代码会在每个时间间隔调用函数，因此会在每个时间间隔请求输入。

Answer 2

如果我不理解，请纠正我。您是否尝试通过用户手动输入表达式并将其视为函数？我找到了this topic，其中解释了如何使用sympy解析公式。您可以尝试使用sympy修改程序。通过这种方式，您应该能够为所有人获得一次方程式。

编辑：如果您的问题只是“如何从输入中获取整个公式...”，您可以尝试使用raw_input（）方法。还要看看here：

Python中Runge-Kutta的方法

2 个答案: