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A fourth-order extrapolated compact difference method for time-fractional convection-reaction-diffusion equations with spatially variable coefficients

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  • Ren, Lei
  • Wang, Yuan-Ming

Abstract

This paper is concerned with numerical methods for a class of time-fractional convection-reaction-diffusion equations. The convection and reaction coefficients of the equation may be spatially variable. Based on the weighted and shifted Grünwald–Letnikov formula for the time-fractional derivative and a compact finite difference approximation for the spatial derivative, we establish an unconditionally stable compact difference method. The local truncation error and the solvability of the resulting scheme are discussed in detail. The stability of the method and its convergence of third-order in time and fourth-order in space are rigorously proved by the discrete energy method. Combining this method with a Richardson extrapolation, we present an extrapolated compact difference method which is fourth-order accurate in both time and space. A rigorous proof for the convergence of the extrapolation method is given. Numerical results confirm our theoretical analysis, and demonstrate the accuracy of the compact difference method and the effectiveness of the extrapolated compact difference method.

Suggested Citation

  • Ren, Lei & Wang, Yuan-Ming, 2017. "A fourth-order extrapolated compact difference method for time-fractional convection-reaction-diffusion equations with spatially variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 1-22.
    • Handle: RePEc:eee:apmaco:v:312:y:2017:i:c:p:1-22
    DOI: 10.1016/j.amc.2017.05.037
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    References listed on IDEAS

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    1. Ji, Cui-cui & Sun, Zhi-zhong, 2015. "The high-order compact numerical algorithms for the two-dimensional fractional sub-diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 775-791.
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    Cited by:

    1. Pulido, M. Aurora P. & Sousa, J. Vanterler C. & de Oliveira, E. Capelas, 2024. "New discretization of ψ-Caputo fractional derivative and applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 135-158.
    2. Roul, Pradip & Prasad Goura, V.M.K. & Agarwal, Ravi, 2019. "A compact finite difference method for a general class of nonlinear singular boundary value problems with Neumann and Robin boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 283-304.
    3. Hajimohammadi, Zeinab & Parand, Kourosh, 2021. "Numerical learning approximation of time-fractional sub diffusion model on a semi-infinite domain," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).

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