euler_approximations.py (adapted from https://gist.github.com/TheVizier/6e8289a52a72090618cea12a253dd8e1)

euler_approximations.py

import math

def f(T,Y):
    """An example first-order ODE, in the form y' = f(t,y).

    Arguments:
    T -- the independent variable
    Y -- the dependent variable
    """
    return math.exp(T)*math.sin(Y)

def euler(f,t_i,y_i,t_f,delta_t):
    """Compute the array of euler approximations of a first-order ODE.

    Arguments:
    f       -- a first-order ODE, in the form y' = f(t,y)
    t_i     -- the initial value of the independent variable
    y_i     -- the initial value of the dependent variable
    t_f     -- the final value of the independent variable
    delta_t -- the linearization step size
    """
    t = float(t_i)
    y = float(y_i)
    dt = float(delta_t)
    steps = round((float(t_f) - t)/dt)
    approx = [ (t,y) ]
    while len(approx) <= steps:
        y = y + f(t,y)*dt
        t = t + dt
        approx.append( (t,y) )
        print(t,y) # added for debugging
    return approx