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This work focuses on integrating a fourth-order compact finite difference scheme (CDS) with a fourth-order exponential time differencing Runge-Kutta method and dimensional splitting (ETDRK4P22-IF), termed the CDS-ETDRK4P22-IF method, for solving nonlinear reaction-diffusion equations (RDEs). The proposed approach employs the ETDRK4P22-IF scheme for temporal discretization following spatial discretization via CDS, resulting in a fully discrete model. Numerical experiments demonstrate that this method achieves both high convergence rates and enhanced computational efficiency.

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1009240
Subject
Runge-Kutta method;
Mathematical analysis;
Nonlinear systems;
Finite difference method;
Discretization;
Reaction-diffusion equations;
Approximation;
Applied mathematics;
Partial differential equations;
Fourier transforms;
Boundary conditions;
Efficiency
Title
A Fourth-order Compact Finite Difference Scheme for Nonlinear Reaction-diffusion Systems
Author
Xiao, Tingting 1 ; Cai, Huiping 2 

1  graduate student of the Guangxi Normal University, Guilin Guangxi 541000, PR. China (e-mail: [email protected]) 
2  associate professor of the College of Mathematics and Statistics in Guangxi Normal University, Guilin 541006, PR. China (Corresponding author, e-mail: [email protected]) 
Publication title
IAENG International Journal of Applied Mathematics; Hong Kong
Volume
55
Issue
9
Pages
2937-2941
Number of pages
6
Publication year
2025
Publication date
Sep 2025
Publisher
International Association of Engineers
Place of publication
Hong Kong
Country of publication
China
Publication subject
Mathematics
ISSN
1992-9978
e-ISSN
1992-9986
Source type
Scholarly Journal
Language of publication
English
Document type
Journal Article
ProQuest document ID
3250127525
Document URL
https://www.proquest.com/scholarly-journals/fourth-order-compact-finite-difference-scheme/docview/3250127525/se-2?accountid=208611
Copyright
© 2025. This work is published under https://creativecommons.org/licenses/by-nc-nd/4.0/ (the"License"). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Last updated
2025-10-07
Database
ProQuest One Academic