Consider the solution of a 2D finite difference solution of the diffusion equation ∇²T = 0 where the boundary conditions correspond to fixed temperatures. What fraction of the entries in the matrix needed to solve this problem are non-zero if there are nx nodes in x and ny nodes in y? Assume that n_x and n_y are large enough so that you can neglect the role of the boundary conditions in your answer. What is the bandwidth of the matrix in this problem? If we wanted to now solve the transient problem, ∂T/∂t = ∇²T, by the method of lines using n_x nodes in x and n_y nodes in y, how many coupled ODEs will we have?