The document reports on the numerical solution of the advection-diffusion equation using the AB2 and RK4 schemes for time integration. Temperature fields and profiles are presented at times of 2.5s, 5s, 7.5s, and 10s for a grid with N=10 and Δt=0.01. A grid refinement study compares errors for grids of 10x10, 20x20, and 40x40 points, finding the error is independent of grid resolution. The RK4 method shows greater accuracy than AB2 as it is fourth order. While errors exist from discretization and machine rounding, a time step of Δt=0.01 was deemed sufficient for this problem.