Question

I’m writing a function for an implicit scheme for solving a specific differential equation. The function looks like this:

import numpy as np

def scheme(N,T):
    y = np.zeros(N+1)          # Array for implicit scheme
    h = T/N                    # Step length
    for i in range(N):
        y[i+1] = y[i] + h*(1+4*y[i])

    print y

I save the file and later import it the usual way, but when I run the scheme function, y = [0 ... 0] where ... are N-1 zeros. It seems like the values are lost in the scope of the for-loop.

If I instead write the whole function in the interpreter (which in my case is Spyder), everything works as it should.

Why doesn’t it work when importing the function from the module?

Answer 1

h = T/N 

is it possible that T and N are both integers and T < N? In that case h = 0 (and y stays all zeros), because it is an integer division (1/2 == 0).

Try to replace this line with

h = 1. * T / N 

and see the results.

y[i+1] = y[i] + h*(1+4*y[i])

can be rewritten as

y[i+1] = y[i] + h + 4 * h * y[i]
               ^^^

which means that for y[i] = 0, the new y[i+1] will be h. If the integer division T/N makes it zero, then it is what you get.