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The finite difference method for Caputo-type parabolic equation with fractional Laplacian: One-dimension case

Author

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  • Hu, Ye
  • Li, Changpin
  • Li, Hefeng

Abstract

In this paper, we present the finite difference method for Caputo-type parabolic equation with fractional Laplacian, where the time derivative is in the sense of Caputo with order in (0, 1) and the spatial derivative is the fractional Laplacian. The Caputo derivative is evaluated by the L1 approximation, and the fractional Laplacian with respect to the space variable is approximated by the Caffarelli–Silvestre extension. The difference schemes are provided together with the convergence and error estimates. Finally, numerical experiments are displayed to verify the theoretical results.

Suggested Citation

  • Hu, Ye & Li, Changpin & Li, Hefeng, 2017. "The finite difference method for Caputo-type parabolic equation with fractional Laplacian: One-dimension case," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 319-326.
    • Handle: RePEc:eee:chsofr:v:102:y:2017:i:c:p:319-326
    DOI: 10.1016/j.chaos.2017.03.038
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    Cited by:

    1. Huizhen Qu & Jianwen Zhou & Tianwei Zhang, 2022. "Three-Point Boundary Value Problems of Coupled Nonlocal Laplacian Equations," Mathematics, MDPI, vol. 10(13), pages 1-18, June.
    2. Ángel García & Mihaela Negreanu & Francisco Ureña & Antonio M. Vargas, 2021. "A Note on a Meshless Method for Fractional Laplacian at Arbitrary Irregular Meshes," Mathematics, MDPI, vol. 9(22), pages 1-9, November.
    3. Chenkuan Li & Changpin Li & Thomas Humphries & Hunter Plowman, 2019. "Remarks on the Generalized Fractional Laplacian Operator," Mathematics, MDPI, vol. 7(4), pages 1-17, March.

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