The aim of this project is to study, implement and deploy an extension of the algebraic formulation for the tau method for the numerical solution of partial differential problems set on domains in $\mathbb{R}^{n}$, $n>2$. This extension is based on an appropriate choice of a basis for the space of polynomials in $\mathbb{R}^{n}$ and on the construction of the algebraic equivalent representation of the problem. An important feature of the required implementation is related to the solution procedure for the necessarily large dimensional linear systems involved.

This effort will be delivered to the scientific community as a crucial building block of the tau toolbox (numerical library).