High-Order Solution of Reaction-Diffusion Systems Applying Compact Finite Difference and Explicit Runge-Kutta Methods

Document Type : Original Article

Authors
Mardan Ameen Pirdawood 1
Younis A. Sabawi 1, 2
Mohammed I. Sadeeq 3
Bashdar O. Hussen 1
Yad A. Kareem 1
Hero M. Hussein 1
Twana A. Ali 1
1 Department of Mathematics, Faculty of Science and Health, Koya University, Koya KOY45, Kurdistan Region, Iraq.
2 College of Information Technology, Imam Ja’afar AL-Sadiq University, Baghdad, Iraq.
3 Department of Mathematics, College of Education, Akre University for Applied Sciences, Kurdistan Region, Iraq.
10.24271/psr.2024.419907.1404
Abstract
This study aims to develop a highly precise method for handling reaction-diffusion systems with Numman boundary conditions. Our approach combines an explicit Runge-Kutta method for the temporal aspect with a 4th order compact finite difference (CFD) technique for spatial dimension. Moreover, we employ a 4th order precise CFD technique to discretize the boundary points. At the core of our methodology lies the utilization of the method of lines (MOL). This approach strategically enables us to effectively incorporate explicit Runge-Kutta methods, known for their fifth-order precision in the temporal domain. Consequently, our approach achieves high-order precision in the temporal and spatial domains, this leads to a noteworthy reduction in the computational costs associated with the scheme. The combination of explicit Runge-Kutta methods and compact finite difference approaches yields a dependable and accurate solution to solve the reaction-diffusion system, according to numerical experiments.
Keywords
Explicit Runge-Kutta method
Compact finite difference method
Reaction-Diffusion System
Crossmark
Subjects
Passer Journal of Basic and Applied Sciences
Volume 6, Issue 2
December 2024
Pages 333-343