2020/03/30 by Mustafa Almushaira, Mustafa, Almushaira, Harish Bhatt +1
Mathematics · #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2003.13569
openalex publication_date 2020/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
To achieve efficient and accurate long-time integration, we propose a fast, accurate, 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 accurate fourth-order modified exponential time differencing Runge-Kutta scheme. The linear stability analysis and various numerical experiments including two-dimensional (2D) Fitzhugh-Nagumo, Gierer-Meinhardt, Gray-Scott and three-dimensional (3D) Schnakenberg models are presented to demonstrate the accuracy, efficiency, and stability of the proposed method.