THE DIFFERENTIAL FORMULATION OF THE TAU METHOD AND ITS ERROR ESTIMATE FOR FOURTH ORDER NON-OVERDETERMINED DIFFERENTIAL EQUATIONS

Abstract

The Tau method has for some time been plagued with the problem of providing a computationally efficient general error estimation procedure for the perturbed problem. In this paper we are concerned with Differential formulation of the Tau methods for numerical solution of initial value problems in non-over determined fourth order ordinary differential equations. To this end, a polynomial is constructed based on the error function associated with polynomial economization which gives a theoretical estimate of the error of the Tau method. In doing so, the number of undetermined constants is kept to a minimum and the resulting polynomial does not require further evaluation in the interval under consideration. The error estimation formula obtained for the class of ODEs is efficient and accurate. Tau Numerical results and details of the algorithm confirm the high accuracy and user-friendly structure of this numerical approach.