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Python function for the exact solution \( \uex(t)=Ie^{-at} \):
def exact_solution(t, I, a):
return I*exp(-a*t)
Quick plotting:
u_e = exact_solution(t, I, a)
plot(t, u, t, u_e)
Problem: \( \uex(t) \) applies the same mesh as \( u^n \) and looks as a piecewise linear function.
Remedy: Introduce a very fine mesh for \( \uex \).
t_e = linspace(0, T, 1001) # fine mesh
u_e = exact_solution(t_e, I, a)
plot(t_e, u_e, 'b-', # blue line for u_e
t, u, 'r--o') # red dashes w/circles
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