An accurate solution of the Poisson equation by the Legendre Tau method

Abstract

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.