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euler.py
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euler.py
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import numpy as np
import matplotlib.pyplot as plt
def euler_method(f, x0, xn, y0, h):
n = int((xn - x0) / h) + 1
t = np.linspace(x0, xn, n)
y = np.zeros_like(t)
y[0] = y0
for i in range(1, n):
y[i] = y[i-1] + h * f(t[i-1], y[i-1])
return t, y
def f(x, y):
return y/x - (y/x)**2
def exact(x):
return x/(1 + np.log(x))
t, P = euler_method(f, 1, 3, 1, 0.25)
u, Q = euler_method(f, 1, 3, 1, 0.1)
v, R = euler_method(f, 1, 3, 1, 0.05)
y_values1 = exact(t)
y_values2 = exact(u)
y_values3 = exact(v)
errors_1 = np.abs(y_values1 - P)
errors_2 = np.abs(y_values2 - Q)
errors_3 = np.abs(y_values3 - R)
# plt.plot(t, errors_1, 'red', label='h = 0.25')
# plt.plot(u, errors_2, 'blue', label='h = 0.1')
# plt.plot(v, errors_3, 'green', label='h = 0.05')
plt.plot(v, y_values3, 'black', label='Analítica')
plt.plot(t, P, 'r', label='h = 0.25')
plt.plot(u, Q, 'b', label='h = 0.1')
plt.plot(v, R, 'g', label='h = 0.05')
plt.legend()
plt.grid(True)
plt.show()