Solving differential and integral equations with Tau method

TL;DR

This paper introduces a novel implementation of the operational Tau method utilizing orthogonal polynomial relations to efficiently solve linear differential and integral equations, demonstrated through numerical applications.

Contribution

The paper presents a new approach for implementing the operational Tau method using three-term relations of orthogonal polynomials for improved computational efficiency.

Findings

Successful numerical solutions of differential equations

Effective use of orthogonal polynomial relations

Demonstrated applicability to integral equations

Abstract

In this work we present a new approach for the implementation of operational Tau method for the solutions of linear differential and integral equations. In our approach we use the three terms relation of an orthogonal polynomial basis to compute the operational matrices. We also give numerical applications of operational matrices to solve differential and integral problems using the operational Tau method.