I am working with Partial Differential Equations, I was able to work through all the questions except the following...

1. In many applications of mathematics in science and finance, we have to solve the Poisson equation: V2 4(x, y) = f, (1) where f is a given function. Consider a simplified problem in a square region by as- suming that f = 2y. Supplement this problem with the following boundary conditions 4(0, y) = 0, 4(1,y) = y, 4(x,0) =0, 4(2,1) =22. (2) (a) On a 2 x 2 grid (2 intervals in each direction), how many unknowns interior values of 4 must be found? (b) Write the equation(s) that must be solved to find the unknown interior value(s) from the previous task (a). (c) Apply a simple Jacobi iteration to the equation(s) from the task (b). How does your answer compare with the exact solution u(x, y) = xy