4. a) Using finite difference method find an approximate solution to Laplace equation Max+Myy 0 in the rectangle: R={(x,y) R²;0<x<4,0≤y<4); where u(x, y) denotes the temperature at a point (x,y) and the boundary conditions are given as follows. u(x,4)=180 for 0<x<4 u,(x, 0) = 0 for 0<x<4 u(0,y) 80 for 0 ≤y<4 u(4.y)=0 for 0≤y<4 Use step size h = k = 1. Use central difference formula for derivative boundary condition. b) Consider the problem having the heat equation: u = xx: 0≤x≤1, OstST with the boundary conditions; u(0,t) = 0, u(1,t) = 0; 0sts and the initial condition; u(x, 0) = x(x-1);0≤x≤1 If hand k compute the numerical solutions of first two time steps away from the initial step using explicit scheme.