$$ \newcommand{\uex}{{u_{\small\mbox{e}}}} \newcommand{\Aex}{{A_{\small\mbox{e}}}} \newcommand{\half}{\frac{1}{2}} \newcommand{\Oof}[1]{\mathcal{O}(#1)} $$

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Comment on array vs scalar computation

Scalar computing of E = sqrt(dt*sum(e**2)):

m = len(u)     # length of u array (alt: u.size)
u_e = zeros(m)
t = 0
for i in range(m):
    u_e[i] = exact_solution(t, a, I)
    t = t + dt
e = zeros(m)
for i in range(m):
    e[i] = u_e[i] - u[i]
s = 0  # summation variable
for i in range(m):
    s = s + e[i]**2
error = sqrt(dt*s)

Obviously, scalar computing

Rule.

Compute on entire arrays (when possible)!

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