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gL 1 Scheme for Solving a Class of Generalized Time-Fractional Diffusion Equations

Author

Listed:
  • Xuhao Li

    (School of Mathematical Sciences, Anhui University, Hefei 230601, China)

  • Patricia J. Y. Wong

    (School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore)

Abstract

In this paper, a numerical scheme based on a general temporal mesh is constructed for a generalized time-fractional diffusion problem of order α . The main idea involves the generalized linear interpolation and so we term the numerical scheme the gL 1 scheme . The stability and convergence of the numerical scheme are analyzed using the energy method. It is proven that the temporal convergence order is ( 2 − α ) for a general temporal mesh. Simulation is carried out to verify the efficiency of the proposed numerical scheme.

Suggested Citation

  • Xuhao Li & Patricia J. Y. Wong, 2022. "gL 1 Scheme for Solving a Class of Generalized Time-Fractional Diffusion Equations," Mathematics, MDPI, vol. 10(8), pages 1-14, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1219-:d:789383
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    References listed on IDEAS

    as
    1. Alikhanov, Anatoly A. & Huang, Chengming, 2021. "A high-order L2 type difference scheme for the time-fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 411(C).
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