ANALYSIS OF NON-SIMULTANEOUS NUMERICAL BLOW-UP IN SYSTEMS OF HEAT EQUATIONS WITH $n$ COMPONENTS AND NONLINEAR BOUNDARY CONDITIONS

Print ISSN: 2319-1023 | Online ISSN: 2582-5461 | Total Downloads :

Volume : 13 , Issue : 1
DOI: https://doi.org/10.56827/JRSMMS.2025.1301.3
Author :
K. Z. Lekporo (Joint Research and Innovation Unit in Mathematics and Digital Sciences, National Polytechnic Institute Houphouet-Boigny, Yamoussoukro BP 2444 , COTE D)
K. B. Edja (Department of Computer and Digital Sciences, Virtual University of Cote dIvoire, 28 BP 536 Abidjan 28 , COTE DIVOIRE)
K. N Guessan (Department of Economic Sciences and Management, Alassane Ouattara University, 01 BP V 18 Bouake 01 , COTE DIVOIRE)
K. A. Toure (Joint Research and Innovation Unit in Mathematics and Digital Sciences, National Polytechnic Institute Houphouet-Boigny, Yamoussoukro BP 2444 , COTE D)

Abstract

This paper concerns the study of a numerical approximation for a system of heat equations with $n$ components and nonlinear boundary conditions. We show that the solution of the semidiscrete problem, obtained by the finite difference method, blows up in finite time. We also establish conditions under which non-simultaneous or simultaneous blow-up occurs for the semidiscrete problem. After proving the convergence of the numerical blow-up time, we conclude by presenting numerical results that illustrate key aspects of our study. 

Keywords and Phrases

System of heat equations, $n$ components, semidiscretization, non-simultaneous blow-up, simultaneous blow-up, convergence, numerical blow-up time, arc-length transformation, Aitken's $\Delta^2$ method.

A.M.S. subject classification

Primary 35K51, 35B55, Secondary 65M06, 65M12.

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