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Legendre-Chebyshev spectral collocation method for two-dimensional nonlinear reaction-diffusion equation with Riesz space-fractional

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  • Abdelkawy, M.A.
  • Alyami, S.A.

Abstract

A high accurate spectral algorithm for two-dimensional nonlinear reaction-diffusion equation with Riesz space-fractional (RF-TNRDEs) is consider. We propose a shifted Legendre Gauss-Lobatto collocation (SL-GL-C) method in conjunction with shifted Chebyshev Gauss-Radau collocation (SC-GR-C) method to solve the RF-TNRDEs. A complete theoretical formulation is presented and numerical examples are given to illustrate the performance and efficiency of the algorithm. The superiority of the scheme to tackle RF-TNRDEs is revealed.

Suggested Citation

  • Abdelkawy, M.A. & Alyami, S.A., 2021. "Legendre-Chebyshev spectral collocation method for two-dimensional nonlinear reaction-diffusion equation with Riesz space-fractional," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    • Handle: RePEc:eee:chsofr:v:151:y:2021:i:c:s0960077921006330
    DOI: 10.1016/j.chaos.2021.111279
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    1. Doha, E.H. & Abd-Elhameed, W.M., 2009. "Efficient spectral ultraspherical-dual-Petrov–Galerkin algorithms for the direct solution of (2n+1)th-order linear differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(11), pages 3221-3242.
    2. Garrappa, Roberto & Popolizio, Marina, 2011. "On the use of matrix functions for fractional partial differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(5), pages 1045-1056.
    3. Bu, Weiping & Tang, Yifa & Wu, Yingchuan & Yang, Jiye, 2015. "Crank–Nicolson ADI Galerkin finite element method for two-dimensional fractional FitzHugh–Nagumo monodomain model," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 355-364.
    4. Giona, Massimiliano & Eduardo Roman, H., 1992. "Fractional diffusion equation for transport phenomena in random media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 185(1), pages 87-97.
    5. Heydari, M.H. & Atangana, A., 2019. "A cardinal approach for nonlinear variable-order time fractional Schrödinger equation defined by Atangana–Baleanu–Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 339-348.
    6. Cheng, Xiujun & Duan, Jinqiao & Li, Dongfang, 2019. "A novel compact ADI scheme for two-dimensional Riesz space fractional nonlinear reaction–diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 452-464.
    7. James W. Kirchner & Xiahong Feng & Colin Neal, 2000. "Fractal stream chemistry and its implications for contaminant transport in catchments," Nature, Nature, vol. 403(6769), pages 524-527, February.
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    Cited by:

    1. Mohammed M. Al-Shomrani & Mohamed A. Abdelkawy & António M. Lopes, 2023. "Spectral Collocation Technique for Solving Two-Dimensional Multi-Term Time Fractional Viscoelastic Non-Newtonian Fluid Model," Mathematics, MDPI, vol. 11(9), pages 1-14, April.

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