4
edits
(updated links to Meyn books) 

:<math>
\begin{bmatrix} u_{11} , u_{21} , \ldots , u_{m1} , u_{12} , u_{22} , \ldots , u_{m2} , \ldots , u_{mn}
\end{bmatrix}^T
This will result in an ''mn'' × ''mn'' linear system:
:<math>
where
<ref>Golub, Gene H. and C. F. Van Loan, ''Matrix Computations, 3rd Ed.'',
The Johns Hopkins University Press, Baltimore, 1996, pages 177–180.</ref>
and <math>\vec{b}</math> is defined by
:<math>
\vec{b} =
\Delta x^2\begin{bmatrix} g_{11} , g_{21} , \ldots , g_{m1} , g_{12} , g_{22} , \ldots , g_{m2} , \ldots , g_{mn}
\end{bmatrix}^T.

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