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L1 scheme on graded mesh for subdiffusion equation with nonlocal diffusion term

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  • Chaudhary, Sudhakar
  • Kundaliya, Pari J.

Abstract

The solution of time fractional partial differential equations in general exhibit a weak singularity near the initial time. In this article we propose a method for solving time fractional diffusion equation with nonlocal diffusion term. The proposed method comprises L1 scheme on graded mesh, finite element method and Newton’s method. We discuss the well-posedness of the weak formulation at discrete level and derive a priori error estimates for fully-discrete formulation in L2(Ω) and H1(Ω) norms. Finally, some numerical experiments are conducted to validate the theoretical findings.

Suggested Citation

  • Chaudhary, Sudhakar & Kundaliya, Pari J., 2022. "L1 scheme on graded mesh for subdiffusion equation with nonlocal diffusion term," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 195(C), pages 119-137.
    • Handle: RePEc:eee:matcom:v:195:y:2022:i:c:p:119-137
    DOI: 10.1016/j.matcom.2022.01.006
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    Keywords

    Nonlocal problem; Initial singularity; L1 scheme; Graded mesh; Error estimate;
    All these keywords.

    JEL classification:

    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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