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Finite Difference Method for Two-Sided Two Dimensional Space Fractional Convection-Diffusion Problem with Source Term

Author

Listed:
  • Eyaya Fekadie Anley

    (School of Mathematics and Statistics, Central South University, Changsha 410083, China
    Department of Mathematics, College of Natural and Computational Science, Arba-Minch University, Arba-Minch 21, Ethiopia)

  • Zhoushun Zheng

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

Abstract

In this paper, we have considered a numerical difference approximation for solving two-dimensional Riesz space fractional convection-diffusion problem with source term over a finite domain. The convection and diffusion equation can depend on both spatial and temporal variables. Crank-Nicolson scheme for time combined with weighted and shifted Grünwald-Letnikov difference operator for space are implemented to get second order convergence both in space and time. Unconditional stability and convergence order analysis of the scheme are explained theoretically and experimentally. The numerical tests are indicated that the Crank-Nicolson scheme with weighted shifted Grünwald-Letnikov approximations are effective numerical methods for two dimensional two-sided space fractional convection-diffusion equation.

Suggested Citation

  • Eyaya Fekadie Anley & Zhoushun Zheng, 2020. "Finite Difference Method for Two-Sided Two Dimensional Space Fractional Convection-Diffusion Problem with Source Term," Mathematics, MDPI, vol. 8(11), pages 1-27, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1878-:d:436932
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    References listed on IDEAS

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    1. Zhao, Yanmin & Bu, Weiping & Huang, Jianfei & Liu, Da-Yan & Tang, Yifa, 2015. "Finite element method for two-dimensional space-fractional advection–dispersion equations," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 553-565.
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