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29 lines
554 B
29 lines
554 B
# Program 02e: Numerical and truncated series solution
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# figure 2.6
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import matplotlib.pyplot as plt
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import numpy as np
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from scipy.integrate import odeint
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def ode(X, t):
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x = X[0]
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y = X[1]
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dxdt = y
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dydt = x-t**2*y
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return [dxdt, dydt]
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X0 = [1, 0]
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t = np.linspace(0, 10, 1000)
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sol = odeint(ode, X0, t)
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x = sol[:, 0]
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y = sol[:, 1]
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fig, ax = plt.subplots()
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ax.plot(t, x, label='Numerical')
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ax.plot(t, 1+t**2/2+t**4/24, 'r-', label='Truncated series')
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plt.xlabel('t')
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plt.ylabel('x')
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plt.xlim(0, 4)
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plt.ylim(0, 4)
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ax.legend()
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plt.show()
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