Use the Finite Difference Method to obtain the numerical solution for the following partial differential equation:
∂"u/∂x" + ∂"u/∂y" = 0,
0 < x < 2, 0 < y < 2
u(0,y) = 0,
u(2,y) = y(2 - y), 0 < y < 2
u(x,0) = 0,
u(x, 2) = {x, 0 < x < 1; 2 - x, 1 ≤ x < 2
a) Consider a mesh size of h = 1/2 with nine interior grid points. Determine nine linear algebraic equations in terms of nine unknowns at these interior grid points. Hand calculations only.
b) Use MATLAB to find a solution for the system of equations obtained in part a.