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

Author

Listed:
  • Almushaira, M.
  • Bhatt, H.
  • Al-rassas, A.M.

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.

Suggested Citation

  • Almushaira, M. & Bhatt, H. & Al-rassas, A.M., 2021. "Fast high-order method for multi-dimensional space-fractional reaction–diffusion equations with general boundary conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 235-258.
    • Handle: RePEc:eee:matcom:v:182:y:2021:i:c:p:235-258
    DOI: 10.1016/j.matcom.2020.11.001
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    Cited by:

    1. Almushaira, Mustafa, 2023. "Efficient energy-preserving eighth-order compact finite difference schemes for the sine-Gordon equation," Applied Mathematics and Computation, Elsevier, vol. 451(C).

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