Journal of Advanced Mathematical Modeling

Journal of Advanced Mathematical Modeling

Fourier spectral approximation for the time-fractional reaction-diffusion Brusselator system

Document Type : Original Paper

Authors
Farzaneh Razavi Sosan 1
Mehdi Ghasemi 2
Mojtaba Fardi 3
1 Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord, IRAN
2 Department of Mathematics, Faculty of Mathematical Sciences, Shahrekord University, Shahrekord 88186-34141, Iran.
3 Department of Applied Mathematics, Faculty of Mathematical Science, Shahrekord University, Shahrekord, P. O. Box 115, Iran
10.22055/jamm.2025.47755.2303
Abstract
This paper introduces a robust numerical method for analyzing the time-fractional reaction-diffusion Brusselator system. The problem is discretized in the spatial direction using the Fourier spectral method and in the temporal direction using a high-order approximation for the Caputo derivative. By leveraging the Fourier spectral method's properties, we can eliminate the second spatial derivatives from the system. The convergence of this method has been proven, and its efficiency and accuracy are demonstrated through various numerical examples. The findings reveal a consistent rate of convergence of two for multiple values of $\alpha$, affirming the method's efficacy in tackling the established system.
Keywords
Time-Fractional
Caputo Derivative
Reaction-Diffiusion Brusselator System
Fourier Spectral Method
Subjects
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  • Receive Date 14 August 2024
  • Revise Date 28 May 2025
  • Accept Date 23 December 2025