Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 2 / 39C / b / Solution

Let $u_j=(u_{1,j},\dots ,u_{m,j}{)}^T$ collect the unknowns in grid column $j$, and define $b_j=h^2(f_{1,j},\dots ,f_{m,j}{)}^T$. The terms within one column form the blockwhile coupling to either adjacent column contributesThe zero boundary values remove all blocks outside the displayed range, so the nine-point finite-difference stencil becomes the block tridiagonal matrix system