In this question, we will consider the numerical approaches for Partial Differential Equations $($PDEs$)$ by considering the solution of the $2$D Poisson Equation. Please refer to the codes provided in the module on CANVAS.

Using a tolerance of Tol. $={10}^{-6},$ providing evidence of your approach in a spreadsheet or word document, investigate the following meshes:

$nx=60,ny=10$

$nx=10,ny=60$

$nx=15,ny=40$

$nx=20,ny=30$

$nx=25,ny=24$

For both the Point$-$Jacobi and Gauss$-$Seidel approaches, highlight the amount of time and number of iterations it takes to achieve convergence for each mesh. What is being varied for each mesh? What conclusions can be drawn?