Collocation for linear problems
Collocation: the locations of the unknowns and approximations are at the same nodes.
Univariate linear TVBVP:
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Matrix linear TVBVP with differencing:
\mathbf{Lu} = \mathbf{r}, \quad \mathbf{L} = \mathbf{D}_{xx} + \mathbf{PD}_{x} + \mathbf{Q}.
Then, add in boundary problems with the deletion matrix \mathbf{E}:
\left[\begin{array}{c} e_0^T\\ \mathbf{EL}\\ e_n^T \end{array}\right] \mathbf{u} = \left[\begin{array}{c} \alpha\\ \mathbf{Er}\\ \beta \end{array}\right].