25. Consider the Helmholtz equation 32H 31:: ' (E Jr?) '92" = 3'3"\" dened in the unit square with homogeneous Dirichlet boundary conditions. [a] Suppose this pmblem is discretized on a uniform grid with step size J1 = l KN + 1) using a ve-point scheme as in Example '11 plus an additional term. Write down the resulting difference method. (b) lCall the resulting mania A. Find a value as: such that for a): -c: to: and h arbitrarilyr small, A is still positive denite, but for 51.32 : m the positive deniteuess is lost. (e) Solve the problem for w = 1 and to = 10 for N = 21' 1 using an appropriate precondi- tioned Krylo'.r subspace method of your choice. or a multigiid method. Use tol = l.e-6. 1iit"erif},F that the last residual norm is below to l and tell us how man}r iterations it took to get there