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\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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Computing the norm of the error

Norms of a function f(t) : \begin{align} ||f||_{L^2} &= \left( \int_0^T f(t)^2 dt\right)^{1/2} \tag{25}\\ ||f||_{L^1} &= \int_0^T |f(t)| dt \tag{26}\\ ||f||_{L^\infty} &= \max_{t\in [0,T]}|f(t)| \tag{27} \end{align}

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