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Abstract problem setting
Consider an abstract differential equation
\mathcal{L}(u)=0\tp
Example: \mathcal{L}(u)=u'(t)+a(t)u(t)-b(t) .
The corresponding discrete equation:
\mathcal{L}_{\Delta}(u) =0\tp
Let now
- u be the numerical solution of the discrete equations,
computed at mesh points: u^n , n=0,\ldots,N_t
- \uex the exact solution of the differential equation
\begin{align*}
\mathcal{L}(\uex)&=0,\\
\mathcal{L}_\Delta(u)&=0\tp
\end{align*}
u is computed at mesh points
