On the generalization of the error and error estimation process of Ortiz’s recursive formulation of the tau method

Abstract

In this paper, the generalization of the Lanczos–Ortiz’s Recursive formulation of the tau method for general non-overdetermined ordinary differential equations is presented. The generalization of the canonical polynomials and their derivatives for both overdetermined and non-overdetermined cases were reported in the earlier works of these authors, thus the emphasis here is on the error and the error estimate procedures. The accuracy of the results were established using some numerical examples and the induction principle.