New implementation of the Tau method for PDEs

In this work we propose an extension of the algebraic formulation for the Tau method for the numerical solution of partial differential problems set on domains in Rn, n>2. This extension is based on an appropriate choice of a basis for the space of polynomials in Rn and on the construction of the algebraic equivalent representation of the problem. Another feature of this implementation is related to the solution procedure for the necessarily large dimensional linear systems involved. We developed for this purpose an adapted LU factorization with a special pivoting strategy to build approximants in the sense of Tau method and to allow the solution of large problems. cal results for differential problems in 2D and 2D will be shown.