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Fast high-order compact difference scheme for the nonlinear distributed-order fractional Sobolev model appearing in porous media

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  • Niu, Yuxuan
  • Liu, Yang
  • Li, Hong
  • Liu, Fawang

Abstract

In this article, we present an efficient numerical algorithm, which combines the fourth-order compact difference scheme (CDS) in space with the fast time two-mesh (TT-M) FBN-θ method, to solve the nonlinear distributed-order fractional Sobolev model appearing in porous media. We also construct the corrected CDS by adding the starting part to deal with the problem with nonsmooth solution and recovery the convergence rate. We derive optimal convergence results and prove the stability of the presented numerical algorithm. Finally, we implement numerical experiments by taking several examples with smooth and nonsmooth solutions to verify the correctness of the theoretical results, the effectiveness of the corrected algorithm and the computational efficiency of the fast algorithm.

Suggested Citation

  • Niu, Yuxuan & Liu, Yang & Li, Hong & Liu, Fawang, 2023. "Fast high-order compact difference scheme for the nonlinear distributed-order fractional Sobolev model appearing in porous media," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 387-407.
    • Handle: RePEc:eee:matcom:v:203:y:2023:i:c:p:387-407
    DOI: 10.1016/j.matcom.2022.07.001
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    References listed on IDEAS

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    1. Kong, Linghua & Zhu, Pengfei & Wang, Yushun & Zeng, Zhankuan, 2019. "Efficient and accurate numerical methods for the multidimensional convection–diffusion equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 179-194.
    2. Yin, Baoli & Liu, Yang & Li, Hong, 2020. "A class of shifted high-order numerical methods for the fractional mobile/immobile transport equations," Applied Mathematics and Computation, Elsevier, vol. 368(C).
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    Cited by:

    1. Chen, Hao & Nikan, Omid & Qiu, Wenlin & Avazzadeh, Zakieh, 2023. "Two-grid finite difference method for 1D fourth-order Sobolev-type equation with Burgers’ type nonlinearity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 248-266.

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