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A new high order ADI numerical difference formula for time-fractional convection-diffusion equation

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  • Wu, Longyuan
  • Zhai, Shuying

Abstract

Based on exponential transformation, quadratic interpolation polynomial and Padé approximation, a new high order finite difference scheme is proposed for solving the two-dimensional (2D) time-fractional convection-dominated diffusion equation (of order α ∈ (0, 1)). The resulting scheme is of (3−α)-order accuracy in time and fourth-order accuracy in space. In order to reduce the amount of computation, the alternating direction implicit (ADI) scheme is further developed. Numerical experiments are given to demonstrate the high accuracy and robustness of our new scheme.

Suggested Citation

  • Wu, Longyuan & Zhai, Shuying, 2020. "A new high order ADI numerical difference formula for time-fractional convection-diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 387(C).
    • Handle: RePEc:eee:apmaco:v:387:y:2020:i:c:s0096300319305478
    DOI: 10.1016/j.amc.2019.124564
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    References listed on IDEAS

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    1. Sun, HongGuang & Li, Zhipeng & Zhang, Yong & Chen, Wen, 2017. "Fractional and fractal derivative models for transient anomalous diffusion: Model comparison," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 346-353.
    2. Zhou, Fengying & Xu, Xiaoyong, 2016. "The third kind Chebyshev wavelets collocation method for solving the time-fractional convection diffusion equations with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 11-29.
    3. Meilan Qiu & Liquan Mei & Dewang Li, 2017. "Fully Discrete Local Discontinuous Galerkin Approximation for Time-Space Fractional Subdiffusion/Superdiffusion Equations," Advances in Mathematical Physics, Hindawi, vol. 2017, pages 1-20, March.
    4. Behroozifar, M. & Sazmand, A., 2017. "An approximate solution based on Jacobi polynomials for time-fractional convection–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 1-17.
    5. Zhang, Juan & Zhang, Xindong & Yang, Bohui, 2018. "An approximation scheme for the time fractional convection–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 305-312.
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