Numerical solution of partial differential equations with variable coefficients with an operational approach to the tau method

Abstract We discuss the numerical solution of linear partial differential equations with variable coefficients by means of an operational approach to Ortiz' recursive formulation of the Tau method. We discuss a procedure which makes it possible to determine the coefficients of a bivariate Tau approximant by means of a reduced set of matrix operations. It involves no discretization of the variables, approximate quadratures or the use of special trial functions. Error surfaces exhibit a remarkable equioscillatory behaviour.