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from typing import Callable

import numpy as np

def explicit_euler(

ode_func: Callable, y0: float, x0: float, step_size: float, x_end: float

) -> np.ndarray:

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

For reference to Euler's method refer to https://en.wikipedia.org/wiki/Euler_method.

Args:

ode_func (Callable): The ordinary differential equation

as a function of x and y.

y0 (float): The initial value for y.

x0 (float): The initial value for x.

step_size (float): The increment value for x.

x_end (float): The final value of x to be calculated.

Returns:

np.ndarray: Solution of y for every step in 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()