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) 

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.