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An approximation scheme for the time fractional convection–diffusion equation

Author

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  • Zhang, Juan
  • Zhang, Xindong
  • Yang, Bohui

Abstract

In this paper, a discrete form is proposed for solving time fractional convection–diffusion equation. Firstly, we obtain a time discrete scheme based on finite difference method. Secondly, we prove that the time discrete scheme is unconditionally stable, and the numerical solution converges to the exact one with order O(τ2−α), where τ is the time step size. Finally, two numerical examples are proposed respectively, to verify the order of convergence.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:335:y:2018:i:c:p:305-312
    DOI: 10.1016/j.amc.2018.04.019
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    Cited by:

    1. Singh, Anup & Das, Subir & Ong, S.H., 2022. "Study and analysis of nonlinear (2+1)-dimensional solute transport equation in porous media," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 491-500.
    2. Jang, Bongsoo & Kim, Hyunju, 2024. "Mapping techniques for collocation method of time-fractional convection–diffusion equations in domains with cracks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 60-79.
    3. 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).

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