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TT-M FE method for a 2D nonlinear time distributed-order and space fractional diffusion equation

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  • Gao, Xinghua
  • Yin, Baoli
  • Li, Hong
  • Liu, Yang

Abstract

In this paper, we consider a fast algorithm to calculate a two-dimensional nonlinear time distributed-order and space fractional diffusion equation, which is called the time two-mesh (TT-M) finite element (FE) method. In time, the TT-M algorithm combined with both the implicit second-order σ backward difference formula and Crank–Nicolson scheme for computing the numerical solution at time t1 is used to speed up the calculation. At the same time, the spatial direction is approximated by the FE method. The detailed analyses of stability and error are also given, and the second-order time convergence accuracy can be arrived at. Finally, some numerical examples are shown to illustrate the effectiveness of our numerical method.

Suggested Citation

  • Gao, Xinghua & Yin, Baoli & Li, Hong & Liu, Yang, 2021. "TT-M FE method for a 2D nonlinear time distributed-order and space fractional diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 117-137.
    • Handle: RePEc:eee:matcom:v:181:y:2021:i:c:p:117-137
    DOI: 10.1016/j.matcom.2020.09.021
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    1. Shi, Dongyang & Yang, Huaijun, 2018. "Superconvergence analysis of finite element method for time-fractional Thermistor problem," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 31-42.
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    4. Yimin Zhao, 2017. "Space as method," City, Taylor & Francis Journals, vol. 21(2), pages 190-206, March.
    5. Zhang, Hui & Jiang, Xiaoyun & Yang, Xiu, 2018. "A time-space spectral method for the time-space fractional Fokker–Planck equation and its inverse problem," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 302-318.
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