Consider the following elliptic PDE: a u au ax2 + x2 1, x = [0, 1]; y = [0, 1] Dy2 Using finite difference methd with step size h = 0.25 for both X- and y-domains, determine u(x, y) at all nodes of the solution mesh with the following boundary conditions: (a) u(x, 0) = u(x, 1) = 1; u(0, y) = u(1, y) = cos(2ny) (b) u (x, 0) = u(x, 1) = 1; du (0, y) au (1, y) = 1 ax Consider the following elliptic PDE: a u au ax2 + x2 1, x = [0, 1]; y = [0, 1] Dy2 Using finite difference methd with step size h = 0.25 for both X- and y-domains, determine u(x, y) at all nodes of the solution mesh with the following boundary conditions: (a) u(x, 0) = u(x, 1) = 1; u(0, y) = u(1, y) = cos(2ny) (b) u (x, 0) = u(x, 1) = 1; du (0, y) au (1, y) = 1 ax