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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Angheluta-Bauer, Luiza / Chen, Xi / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi / Yang, Xu

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Volume 16, Issue 6


Robust IMEX Schemes for Solving Two-Dimensional Reaction–Diffusion Models

Kolade M. Owolabi
  • Corresponding author
  • Department of Mathematical Sciences, Federal University of Technology, Akure PMB 704, Akure, Ondo State, Nigeria
  • Department of Mathematics and Applied Mathematics, University of the Western Cape, Private Bag X17, Bellville 7535, South Africa
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Published Online: 2015-09-05 | DOI: https://doi.org/10.1515/ijnsns-2015-0004


In this paper, numerical simulations of two-dimensional reaction–diffusion (for single and multi-species) models are considered for pattern formation processes. The nature of our problems permits the use of two classical approaches. These semi-linear partial differential equations are split into a linear equation which contains the highly stiff part of the problem, and a nonlinear part that is expected to be varying slowly than the linear part. For the spatial discretization, we introduce higher-order symmetric finite difference scheme, and the resulting ordinary differential equations are then solved with the use of the family of implicit–explicit (IMEX) schemes. Stability properties of these schemes as well as the linear stability analysis of the problems are well presented. Numerical examples and results are also given to illustrate the accuracy and implementation of the methods.

Keywords: autocatalysis; Ginzburg–Landau model; Gray-Scott model; systems; IMEX methods; pattern formation; predator–prey; reaction–diffusion; stability

MSC® 2010: 92B05; 92C15; 35K55; 65M20; 76R50


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About the article

Received: 2015-01-08

Accepted: 2015-08-07

Published Online: 2015-09-05

Published in Print: 2015-10-01

Funding: This research was supported by the South African National Research Foundation.

Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 16, Issue 6, Pages 271–284, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2015-0004.

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