Review of Recursive and Operational Approaches of the Tau Method With a New Extension

Abstract

This is a review paper that briefly represents the recursive and operational approaches to the Tau method on solving ordinary differential and integro-differential equations with suitable initial or boundary conditions, and we discuss a new extension of the method on solving a class of Abel Volterra integral equations which can be also used for solving fractional differential equations. Extension of height and canonical polynomials are introduced. Illustrative examples are given in each case to clarify the performance and structural properties of the method.