### Wave Equation : Triangular Pulse

Let u(x; y) be the solution on 0 < x < 2 and 0 < y < 2 of uxx + uyy = 0 with u(0, y) = u(2, y) = u(x, 2) = 0 and u(x, 0) = f(x) the triangular pulse with f(0) = f(2) = 0 and f(1) = 2. f(x) = {2x 0<x<1 {-2x+4 1<x<2 Let uj,k = u(j/2; k/2) for j = 1; 2; 3 and k = 1; 2; 3 as obtained by the numerical method. (a)