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import numpy as np

def explicit_euler(ode_func, y0, x0, step_size, x_end):

"""

Calculate numeric solution at each step to an ODE using Euler's Method

https://en.wikipedia.org/wiki/Euler_method

Arguments:

ode_func -- The ode as a function of x and y

y0 -- the initial value for y

x0 -- the initial value for x

stepsize -- the increment value for x

x_end -- the end value for x

>>> # the exact solution is math.exp(x)

>>> def f(x, y):

... return y

>>> y0 = 1

>>> y = explicit_euler(f, y0, 0.0, 0.01, 5)

>>> y[-1]

144.77277243257308

"""

N = int(np.ceil((x_end - x0) / step_size))

y = np.zeros((N + 1,))

y[0] = y0

x = x0

for k in range(N):

y[k + 1] = y[k] + step_size * ode_func(x, y[k])

x += step_size

return y

if __name__ == "__main__":

import doctest

doctest.testmod()