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48 lines
1.2 KiB
Python
48 lines
1.2 KiB
Python
from collections.abc import Callable
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import numpy as np
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def explicit_euler(
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ode_func: Callable, y0: float, x0: float, step_size: float, x_end: float
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) -> np.ndarray:
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"""Calculate numeric solution at each step to an ODE using Euler's Method
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For reference to Euler's method refer to https://en.wikipedia.org/wiki/Euler_method.
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Args:
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ode_func (Callable): The ordinary differential equation
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as a function of x and y.
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y0 (float): The initial value for y.
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x0 (float): The initial value for x.
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step_size (float): The increment value for x.
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x_end (float): The final value of x to be calculated.
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Returns:
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np.ndarray: Solution of y for every step in x.
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>>> # the exact solution is math.exp(x)
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>>> def f(x, y):
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... return y
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>>> y0 = 1
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>>> y = explicit_euler(f, y0, 0.0, 0.01, 5)
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>>> y[-1]
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144.77277243257308
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"""
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N = int(np.ceil((x_end - x0) / step_size))
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y = np.zeros((N + 1,))
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y[0] = y0
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x = x0
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for k in range(N):
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y[k + 1] = y[k] + step_size * ode_func(x, y[k])
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x += step_size
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return y
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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