In [7]:

import numpy as np
import matplotlib.pyplot as pt

We'll integrate

\[ y'=\alpha y\]

with \(y'(0) = 1\),

using forward Euler.

In [119]:

# 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

In [120]:

t_values = [0]
y_values = [1]

def f(y):
    return alpha * y

In [121]:

while t_values[-1] < final_t:
    t_values.append(t_values[-1] + h)
    y_values.append(y_values[-1] + h*f(y_values[-1]))

In [122]:

mesh = np.linspace(0, final_t, 100)
pt.plot(t_values, y_values)
pt.plot(mesh, np.exp(alpha*mesh), label="true")
pt.legend()

Out[122]:

<matplotlib.legend.Legend at 0x78d2550>

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