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42 lines
891 B
Python
42 lines
891 B
Python
import numpy as np
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def explicit_euler(ode_func, y0, x0, stepsize, x_end):
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"""
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Calculate numeric solution at each step to an ODE using Euler's Method
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https://en.wikipedia.org/wiki/Euler_method
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Arguments:
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ode_func -- The ode as a function of x and y
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y0 -- the initial value for y
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x0 -- the initial value for x
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stepsize -- the increment value for x
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x_end -- the end value for 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)/stepsize))
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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] + stepsize*ode_func(x, y[k])
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x += stepsize
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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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