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Local discontinuous Galerkin method for multi-term variable-order time fractional diffusion equation

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  • Wei, Leilei
  • Wang, Huanhuan

Abstract

This paper presents an effective numerical method for multi-term variable-order time fractional diffusion equations with the variable-order fractional derivative. The local discontinuous Galerkin method and the finite difference method are used in the spatial and temporal directions, respectively. We prove that the scheme is unconditional stable and convergent with O(hs+1+(Δt)2−r), where r=max{ɛ(t)}. s, h, Δt are the degree of piecewise polynomials, the space step sizes, and the time step sizes, respectively. Some numerical experiments are used to illustrate the effectiveness and applicability of the scheme.

Suggested Citation

  • Wei, Leilei & Wang, Huanhuan, 2023. "Local discontinuous Galerkin method for multi-term variable-order time fractional diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 685-698.
    • Handle: RePEc:eee:matcom:v:203:y:2023:i:c:p:685-698
    DOI: 10.1016/j.matcom.2022.07.017
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    1. Chen, Ting & Wang, Derong, 2020. "Combined application of blockchain technology in fractional calculus model of supply chain financial system," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    2. Haq, Sirajul & Ghafoor, Abdul & Hussain, Manzoor, 2019. "Numerical solutions of variable order time fractional (1+1)- and (1+2)-dimensional advection dispersion and diffusion models," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 107-121.
    3. Li, Changpin & Wang, Zhen, 2020. "The discontinuous Galerkin finite element method for Caputo-type nonlinear conservation law," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 169(C), pages 51-73.
    4. Wei, Leilei & Li, Wenbo, 2021. "Local discontinuous Galerkin approximations to variable-order time-fractional diffusion model based on the Caputo–Fabrizio fractional derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 280-290.
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