mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-18 01:00:15 +00:00
7f04e5cd34
* spelling corrections * review * improved documentation, removed redundant variables, added testing * added type hint * camel case to snake case * spelling fix * review * python --> Python # it is a brand name, not a snake * explicit cast to int * spaces in int list * "!= None" to "is not None" * Update comb_sort.py * various spelling corrections in documentation & several variables naming conventions fix * + char in file name * import dependency - bug fix Co-authored-by: John Law <johnlaw.po@gmail.com>
41 lines
898 B
Python
41 lines
898 B
Python
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()
|