A matrix formulation of the Tau method for the numerical solution of non-linear problems

TL;DR

This paper introduces the shifted Bessel Tau (SBT) method, a new numerical approach that uses operational matrices of shifted Bessel polynomials to efficiently and accurately solve higher-order ODEs by reducing them to algebraic systems.

Contribution

The paper develops a novel shifted Bessel Tau method with operational matrices, providing a simple and accurate technique for solving higher-order ODEs.

Findings

The SBT method is computationally simple.

The SBT method yields highly accurate solutions.

Comparisons show it outperforms some existing methods.

Abstract

The purpose of this research is to propose a new approach named the shifted Bessel Tau (SBT) method for solving higher-order ordinary differential equations (ODE). The operational matrices of derivative, integral and product of shifted Bessel polynomials on the interval [a, b] are calculated. These matrices together with the Tau method are utilized to reduce the solution of the higher-order ODE to the solution of a system of algebraic equations with unknown Bessel coefficients. The comparisons between the results of the present work and other the numerical method are shown that the present work is computationally simple and highly accurate.