THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

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Mohd Kashif

,

Prashant Pandey

,

Hossein Jafari

A NOVEL NUMERICAL MANNER FOR NON-LINEAR COUPLED VARIABLE ORDER REACTION-DIFFUSION EQUATION

ABSTRACT
In this work, an efficient variable order Bernstein collocation technique, which is based on Bernstein polynomials, is applied to a non-linear coupled system of variable order reaction-diffusion equations with given initial and boundary conditions. The operational matrix of Bernstein polynomials is derived for variable order derivatives w.r.t. time and space. The Bernstein operational matrix and collocation technique are applied to the concerned non-linear physical model to achieve a system of non-linear algebraic equations, which are further solved by using Newton method. A few examples are presented to demonstrate the accuracy and stability of the scheme by comparing L2 and L∞ norm errors between the obtained numerical solutions and existing solutions. The important feature of this article is the graphical exhibitions of the effects of variable order derivatives on the solutions of the considered non-linear coupled reaction-diffusion equation for different particular cases.
KEYWORDS
variable order derivatives, diffusion equation, Bernstein polynomials, convergence analysis, error bounds
PAPER SUBMITTED: 2022-06-11
PAPER REVISED: 2022-06-24
PAPER ACCEPTED: 2022-07-04
PUBLISHED ONLINE: 2023-04-08
DOI REFERENCE: https://doi.org/10.2298/TSCI23S1353K
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE Special issue 1, PAGES [353 - 363]
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A novel numerical manner for non-linear coupled variable order reaction-diffusion equation

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence