A Line-Tau Collocation Method for Partial Differential Equations

Abstract

This paper deals with the numerical solution of second order linear partial differential equations with the use of the method of lines coupled with the tau collocation method. The method of lines is used to convert the partial differential equation (PDE) to a sequence of ordinary differential equations (ODEs) which is then solved by the tau collocation method to obtain an approximate continuous solution in the spatial variable x at a fixed t-level. The choice of the tau collocation method over the tau method itself was due to the presence of some transcedental functions since both methods produce approximate results. Numerical evidences show that the method performs favourably well.

Keywords: Collocation method, Partial differential equations, Tau method, Method of Lines