Comprehensive Numerical Analysis of Time-Fractional Reaction–Diffusion Models with Applications to Chemical and Biological Phenomena

Kolade M. Owolabi (), Sonal Jain, Edson Pindza and Eben Mare
Additional contact information
Kolade M. Owolabi: Department of Mathematical Sciences, Federal University of Technology, Akure PMB 704, Ondo State, Nigeria
Sonal Jain: School of Technology, Woxsen University, Hyderabad 502345, Telangana, India
Edson Pindza: Department of Decision Sciences, College of Economic and Management Sciences, University of South Africa (UNISA), Pretoria 0003, South Africa
Eben Mare: Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa

Mathematics, 2024, vol. 12, issue 20, 1-26

Abstract: This paper aims to present a robust computational technique utilizing finite difference schemes for accurately solving time fractional reaction–diffusion models, which are prevalent in chemical and biological phenomena. The time-fractional derivative is treated in the Caputo sense, addressing both linear and nonlinear scenarios. The proposed schemes were rigorously evaluated for stability and convergence. Additionally, the effectiveness of the developed schemes was validated through various linear and nonlinear models, including the Allen–Cahn equation, the KPP–Fisher equation, and the Complex Ginzburg–Landau oscillatory problem. These models were tested in one-, two-, and three-dimensional spaces to investigate the diverse patterns and dynamics that emerge. Comprehensive numerical results were provided, showcasing different cases of the fractional order parameter, highlighting the schemes’ versatility and reliability in capturing complex behaviors in fractional reaction–diffusion dynamics.

Keywords: reaction–diffusion; fractional derivatives; numerical simulations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/20/3251/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/20/3251/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:20:p:3251-:d:1500717

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().