Bernstein Tau Method for Bessel and Diffusion Equations

V. Appala Naidu*, G. V. S. R. Deekshitulu **
* Department of Mathematics, Government College for Men, Kadapa, Andhra Pradesh, India.
** Department of Mathematics, University College of Engineering Kakinada, Kakinada, Andhra Pradesh, India.
Periodicity:January - June'2020
DOI : https://doi.org/10.26634/jmat.9.1.17604

Abstract

Some physical problems in science and engineering are modelled by the parabolic partial differential equations with nonlocal boundary specifications. The aim of the present paper is to solve the higher-order linear differential and partial differential equations using Bernstein operational matrix of differentiation and Tau method. The nature of simplicity and efficiency of numerical technique has been demonstrated by considering Bessel equation of order zero and diffusion equation. The novelty of the work in this paper is to obtain an approximate solution to second order parabolic differential equation using an algorithm involving Bernstein basis polynomials and Tau method. The approximate solutions obtained by the present method are compared with the exact solutions, and the numerical results of other methods.

Keywords

Bernstein Polynomial, Tau Method, Bessel Differential Equation, Diffusion Equation.

How to Cite this Article?

Naidu, V. A., and Deekshitulu, G. V. S. R. (2020). Bernstein Tau Method for Bessel and Diffusion Equations. i-manager's Journal on Mathematics, 9(1), 28-37. https://doi.org/10.26634/jmat.9.1.17604

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