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

Authors

  • K. Z. Lekporo Joint Research and Innovation Unit in Mathematics and Digital Sciences, National Polytechnic Institute Houphouët-Boigny, Yamoussoukro BP 2444 , COTE D'IVOIRE Author
  • K. B. Edja Department of Computer and Digital Sciences, Virtual University of Côte d'Ivoire, 28 BP 536 Abidjan 28 , COTE D'IVOIRE Author
  • K. N'Guessan Department of Economic Sciences and Management, Alassane Ouattara University, 01 BP V 18 Bouaké 01 , COTE D'IVOIRE Author
  • K. A. Touré Joint Research and Innovation Unit in Mathematics and Digital Sciences, National Polytechnic Institute Houphouët-Boigny, Yamoussoukro BP 2444 , COTE D'IVOIRE Author

DOI:

https://doi.org/10.56827/JRSMMS.2025.1301.3

Keywords:

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

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.

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Published

2025-12-30

Issue

Vol. 13 No. 1 (2025): Journal of Ramanujan Society of Mathematics and Mathematical Sciences

Section

Research Article