import numpy as np
import matplotlib.pyplot as pt
We'll integrate
\[ y'=\alpha y\]
with \(y'(0) = 1\),
using forward Euler.
# alpha = 1; h = 0.1; final_t = 20
# alpha = -1; h = 0.1; final_t = 20
#alpha = -1; h = 1; final_t = 20
#alpha = -1; h = 1.5; final_t = 20
#alpha = -1; h = 2; final_t = 20
alpha = -1; h = 2.5; final_t = 20
t_values = [0]
y_values = [1]
def f(y):
return alpha * y
while t_values[-1] < final_t:
t_values.append(t_values[-1] + h)
y_values.append(y_values[-1] + h*f(y_values[-1]))
mesh = np.linspace(0, final_t, 100)
pt.plot(t_values, y_values)
pt.plot(mesh, np.exp(alpha*mesh), label="true")
pt.legend()