An accurate solution of the Poisson equation by the Chebyshev-Tau method

A new Tau method is presented for the two-dimensional Poisson equation. Comparison of the results for the test problem u(x, y) = sin(4πx) sin(4πy) with those computed by Haidvogel and Zang, using the matrix diagonalization method, and Dang-Vu and Delcarte, using the Chebyshev collocation method, indicates that our method would be more accurate.