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explicit_euler.py
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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()