Consider the solution to the diffusion equation

on a 4 × 4 rectangular grid with equal spacing in the x and y directions. The boundary conditions for the problem are

Using the global index k and the ordering of equations and unknowns in order of the index k, determine the non-zero entries on the seventh, eighth, and fourteenth rows of the Jacobian required to solve this problem. You should clearly state the corresponding residual equations, since the form of the Jacobian will depend on how you write the residual.

Vc=0