11. (a)(i) Solve uxx+uyy=0 over the square mesh of side 4 units; satisfying the
following conditions.
u(x,0)=3x for 0 = x = 4
u(x,4)=x² for 0 = x = 4
u(0,y)=0 for 0 = y = 4 ; u(4,y)=12+y for 0 = y = 4
(ii) Solve d²u / d x ² - 2.du / dt =0 given u(0,t)=0, u(4,t)=0,u(x,0)=x(4-x).
Assume h=1. Find the values of u upto t=5.