Method of Runge-Kutta in Python

Question

I wrote a code about runge-kutta method in python, but every time when the program realizes any calculus the program require the differential equation.

this is my code:

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

Example using the equation 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]

What should i do to enter only once the differential equation to program calculate all?

score 1 · Accepted Answer · edited May 23 '17 at 12:13

1

Correct me if I don't have understood. Are you trying to get an expression manually-typed by the user and treat that as a function? I found this topic where it explains how to parse a formula using sympy. You can try to modify your program using sympy. In this manner you should be able to get your equation once for all.

EDIT: if your problem is just "how to get the entire formula once from input..." you can just try to use the raw_input() method. Have also a look here:

edited May 23 '17 at 12:13

Community

1
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answered Jul 30 '15 at 09:14

BY0B

99
1
9

well you must ask this is comment and not in answer – VedantK Jul 30 '15 at 09:22
I provide two answers, so I don't think I'm wrong pressing the "Answer Button". Thank you for your constructive comment, btw. – BY0B Jul 30 '15 at 09:28
Thank you very much, I had not thought to use the sympy. – Jeff Jul 30 '15 at 16:52

score 1 · Answer 2 · answered Jul 30 '15 at 09:41

You have to move the the equation input code out of your function f(x,y)

Ask for the equations to be input in the same block as you are asking for all the other input.

As it stands your code calls the function at every time interval so will ask for input at every time interval.

Method of Runge-Kutta in Python

2 Answers2