What is the most pythonic way to solve a differential equation using the Euler method?

Question

For example, with this differential equation, how can I do it in a pythonic way?

dx/dt=f(x,t)

I have a way to do it, but I think this is not the most pythonic way:

import numpy as np
dt=0.01
N_iter=10./dt
def f(x,t):
 return x**2*t#insert your favorite function here
x=np.zeros(N_iter)
for i in range(N_iter-1):
 x[i+1]=x[i]+dt*f(x[i],i*dt)

• Gareth Rees: What was wrong with scipy.integrate?
• Quentin Pradet: What makes you think the code isn't Pythonic? (apart from PEP8 issues)
• gota: Well I thought that there was only one pythonic way to do something and I was wondering if I was doing it right. The problem with 'scipy.integrate' is that I must do each step in turn inside a loop.
• Gareth Rees: @NunoCalaim: Have you looked at scipy.integrate.odeint?

Answer 1

Using a for loop is not an unpythonic way at all. Instead, an Euler method could be implemented with a recursive function, but it not necessary and less optimized in Python.

However, methods for vectorizing recursive sequences are discussed on the numpy-discussion mailing-list. I encourage you to use structures like for loops in such situations. You will minimize the risk of errors by writing simple and concise codes.