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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

An Unconditionally Stable Numerical Algorithm for Two-Dimensional Convection-Diffusion-Reaction Equations

Journal of Applied Nonlinear Dynamics 13(1) (2024) 37--47 | DOI:10.5890/JAND.2024.03.004

Chinedu Nwaigwe

Department of Mathematics, Rivers State University, Nigeria

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Abstract

An unconditionally stable finite difference scheme is developed and fully analyzed for two-dimensional convection-diffusion-reaction equations with nonlinear coefficients and external sources. The well-known difficulty in obtaining a stable second-order discretization of the convection term is resolved by first adopting a central discretization in space. The semi-discrete convection term is split into the positive and negative parts. Then a non-standard time-integration is proposed - by treating one part implicitly and the other explicitly. This allowed to maintain numerical stability, retain compactness of the stencil and avoid division by the diffusion coefficient, hence can be applied to purely convection (zero diffusion) problems. The solvability, consistency and stability of the scheme are established. Numerical results are provided to verify the theoretical properties. [\hfill Convection-diffusion equations\par \hfill Nonlinear coefficients\par \hfill Convergence analysis\par \hfill Stability\par \hfill Consistency\par \hfill Implicit scheme\par \hfill Two-sided bounds\par][Antonio Lopes][6 May 2022][25 October 2022][1 January 2024][2024 L\&H Scientific Publishing, LLC. All rights reserved.] \maketitle \thispagestyle{firstpage} \renewcommand{\baselinestretch}{1} \normalsize \section{Introduction}\label{sec-intro} \begin{figure

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