Fast high-order method for multi-dimensional space-fractional reaction–diffusion equations with general boundary conditions

M. Almushaira, H. Bhatt and A.M. Al-rassas

Mathematics and Computers in Simulation (MATCOM), 2021, vol. 182, issue C, 235-258

Abstract: To achieve the efficient and accurate long-time integration, we propose a fast and stable high-order numerical method for solving fractional-in-space reaction–diffusion equations. The proposed method is explicit in nature and utilizes the fourth-order compact finite difference scheme and matrix transfer technique (MTT) in space with FFT-based implementation. Time integration is done through the modified fourth-order exponential time differencing Runge–Kutta scheme. The linear stability analysis and various numerical experiments including two-dimensional (2D) Fitzhugh–Nagumo, Allen–Cahn, Gierer–Meinhardt, Gray–Scott and three-dimensional (3D) Schnakenberg models are presented to demonstrate the accuracy, efficiency, and stability of the proposed method.

Keywords: Space-fractional reaction–diffusion; Discrete fast transform; Matrix transfer technique; Exponential time differencing (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:182:y:2021:i:c:p:235-258

DOI: 10.1016/j.matcom.2020.11.001

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