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Numerical Finite-Difference Approximations of a Coupled Reaction-Diffusion System with Gradient Terms

This study focuses on the derivation of explicit and implicit finite difference formulas.The objective of this study is to derive an estimation of the blow-up time for a coupled reaction-diffusion system incorporating gradient terms, employing numerical finite difference approximations. Furthermore,...

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Bibliographic Details
Published in:European journal of pure and applied mathematics 2024-07, Vol.17 (3), p.1516-1538
Main Authors: Khalil, Manar, Hashim, Ishak, Rasheed, Maan, Samat, Faieza, Momani, Shaher
Format: Article
Language:English
Online Access:Get full text
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Summary:This study focuses on the derivation of explicit and implicit finite difference formulas.The objective of this study is to derive an estimation of the blow-up time for a coupled reaction-diffusion system incorporating gradient terms, employing numerical finite difference approximations. Furthermore, an examination is conducted on the consistency, stability, and convergence of the proposed schemes. Additionally, the study presents two numerical experiments. In each instance, the numerical blow-up time is calculated benefit the suggested methodologies, employing varying space steps and non-fixed time-stepping. The numerical findings obtained demonstrate that the blow-up time sequence exhibits convergence as the space step decreases. Moreover, thenumerical orders of convergence for the blow-up time goes well with the theoretical orders observed in the numerical solutions.
ISSN:1307-5543
1307-5543
DOI:10.29020/nybg.ejpam.v17i3.5246