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A meshless method based on Point Interpolation Method (PIM) for the space fractional diffusion equation

Author

Listed:
  • Liu, Q.
  • Liu, F.
  • Gu, Y.T.
  • Zhuang, P.
  • Chen, J.
  • Turner, I.

Abstract

This paper aims to develop a meshless approach based on the Point Interpolation Method (PIM) for numerical simulation of a space fractional diffusion equation. Two fully-discrete schemes for the one-dimensional space fractional diffusion equation are obtained by using the PIM and the strong-forms of the space diffusion equation. Numerical examples with different nodal distributions are studied to validate and investigate the accuracy and efficiency of the newly developed meshless approach.

Suggested Citation

  • Liu, Q. & Liu, F. & Gu, Y.T. & Zhuang, P. & Chen, J. & Turner, I., 2015. "A meshless method based on Point Interpolation Method (PIM) for the space fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 930-938.
    • Handle: RePEc:eee:apmaco:v:256:y:2015:i:c:p:930-938
    DOI: 10.1016/j.amc.2015.01.092
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    Cited by:

    1. H. Ghafouri & M. Ranjbar & A. Khani, 2020. "The Use of Partial Fractional Form of A-Stable Padé Schemes for the Solution of Fractional Diffusion Equation with Application in Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 695-709, December.
    2. Zieniuk, Eugeniusz, 2017. "Approximation of the derivatives of solutions in a normalized domain for 2D solids using the PIES methodAuthor-Name: Bołtuć, Agnieszka," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 138-155.
    3. Saberi Zafarghandi, Fahimeh & Mohammadi, Maryam & Babolian, Esmail & Javadi, Shahnam, 2019. "Radial basis functions method for solving the fractional diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 224-246.
    4. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    5. Zeng, Yunhua & Tan, Zhijun, 2022. "Two-grid finite element methods for nonlinear time fractional variable coefficient diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 434(C).
    6. Y. Esmaeelzade Aghdam & H. Mesgarani & A. Adl & B. Farnam, 2023. "The Convergence Investigation of a Numerical Scheme for the Tempered Fractional Black-Scholes Model Arising European Double Barrier Option," Computational Economics, Springer;Society for Computational Economics, vol. 61(2), pages 513-528, February.

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