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A Stable Numerical Scheme for a Lengyel-Epstein Reaction Diffusion Model.

We study a reaction diffusion Lengyel-Epstein system, which describes the formation of chemical Turing patterns. An unconditionally stable semi-implicit difference scheme is proposed for the system. It is proven that the numerical scheme is uniquely solvable and inherits the properties of the origin...

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Published in:Journal of the Utah Academy of Sciences, Arts & Letters Vol. 102; p. 383
Main Author: Han, Jianlong
Format: Article
Published: Utah Academy of Sciences, Arts & Letters 2025
Subjects:
Reaction-diffusion equations
Finite difference method
Equilibrium
Discretization methods
Stability theory
Pattern formation (Physical sciences)
Online Access:View this record in EBSCOhost
Summary:We study a reaction diffusion Lengyel-Epstein system, which describes the formation of chemical Turing patterns. An unconditionally stable semi-implicit difference scheme is proposed for the system. It is proven that the numerical scheme is uniquely solvable and inherits the properties of the original system. The long-term behavior of the numerical solution is analyzed.