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Nonuniform difference schemes for multi-term and distributed-order fractional parabolic equations with fractional Laplacian

Author

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  • Fardi, M.
  • Zaky, M.A.
  • Hendy, A.S.

Abstract

In this paper, the multi-term temporal fractional order and temporal distributed-order parabolic equations with fractional Laplacian are numerically investigated. Several unconditional stable difference schemes based on non-uniform meshes for solving these differential equations are provided. We find that the constructed nonuniform difference schemes are convergent and it has been shown that the temporal convergence rate is faster and more accurate compared to the uniform difference schemes in case of nonsmooth solutions with respect to time. Some numerical examples are given to verify the theoretical findings.

Suggested Citation

  • Fardi, M. & Zaky, M.A. & Hendy, A.S., 2023. "Nonuniform difference schemes for multi-term and distributed-order fractional parabolic equations with fractional Laplacian," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 614-635.
    • Handle: RePEc:eee:matcom:v:206:y:2023:i:c:p:614-635
    DOI: 10.1016/j.matcom.2022.12.009
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    References listed on IDEAS

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    1. Hafez, Ramy M. & Zaky, Mahmoud A. & Hendy, Ahmed S., 2021. "A novel spectral Galerkin/Petrov–Galerkin algorithm for the multi-dimensional space–time fractional advection–diffusion–reaction equations with nonsmooth solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 678-690.
    2. Luo, Man & Qiu, Wenlin & Nikan, Omid & Avazzadeh, Zakieh, 2023. "Second-order accurate, robust and efficient ADI Galerkin technique for the three-dimensional nonlocal heat model arising in viscoelasticity," Applied Mathematics and Computation, Elsevier, vol. 440(C).
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    Cited by:

    1. Ji Lin & Sergiy Reutskiy & Yuhui Zhang & Yu Sun & Jun Lu, 2023. "The Novel Analytical–Numerical Method for Multi-Dimensional Multi-Term Time-Fractional Equations with General Boundary Conditions," Mathematics, MDPI, vol. 11(4), pages 1-26, February.

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