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A Second-Order Accurate Numerical Approximation for a Two-Sided Space-Fractional Diffusion Equation

Author

Listed:
  • Taohua Liu

    (School of Science, Shaoyang University, Shaoyang 422000, China)

  • Xiucao Yin

    (School of Science, Shaoyang University, Shaoyang 422000, China)

  • Yinghao Chen

    (School of Mathematics and Statistics, Central South University, Changsha 410083, China
    Eastern Institute for Advanced Study, Yongriver Institute of Technology, Ningbo 315201, China)

  • Muzhou Hou

    (School of Mathematics and Statistics, Central South University, Changsha 410083, China)

Abstract

In this paper, we investigate a practical numerical method for solving a one-dimensional two-sided space-fractional diffusion equation with variable coefficients in a finite domain, which is based on the classical Crank-Nicolson (CN) method combined with Richardson extrapolation. Second-order exact numerical estimates in time and space are obtained. The unconditional stability and convergence of the method are tested. Two numerical examples are also presented and compared with the exact solution.

Suggested Citation

  • Taohua Liu & Xiucao Yin & Yinghao Chen & Muzhou Hou, 2023. "A Second-Order Accurate Numerical Approximation for a Two-Sided Space-Fractional Diffusion Equation," Mathematics, MDPI, vol. 11(8), pages 1-15, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1838-:d:1122107
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    References listed on IDEAS

    as
    1. Li, Shengyue & Zhou, Zhaojie, 2019. "Fractional spectral collocation method for optimal control problem governed by space fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 331-347.
    2. Raberto, Marco & Scalas, Enrico & Mainardi, Francesco, 2002. "Waiting-times and returns in high-frequency financial data: an empirical study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 749-755.
    3. Feng, L.B. & Zhuang, P. & Liu, F. & Turner, I., 2015. "Stability and convergence of a new finite volume method for a two-sided space-fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 52-65.
    4. Ebru Ozbilge & Fatma Kanca & Emre Özbilge, 2022. "Inverse Problem for a Time Fractional Parabolic Equation with Nonlocal Boundary Conditions," Mathematics, MDPI, vol. 10(9), pages 1-8, April.
    5. James W. Kirchner & Xiahong Feng & Colin Neal, 2000. "Fractal stream chemistry and its implications for contaminant transport in catchments," Nature, Nature, vol. 403(6769), pages 524-527, February.
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