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

1
School of Mathematics and Statistics, Central South University, Changsha 410083, China
2
Department of Mathematics, College of Natural and Computational Science, Arba-Minch University, Arba-Minch 21, Ethiopia
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(11), 1878; https://doi.org/10.3390/math8111878
Received: 17 August 2020 / Revised: 22 September 2020 / Accepted: 26 September 2020 / Published: 29 October 2020
(This article belongs to the Special Issue Fractional Integrals and Derivatives: “True” versus “False”)
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. View Full-Text
Keywords: Crank–Nicolson scheme; weighted Shifted Grünwald–Letnikov approximation; space fractional convection-diffusion model; stability analysis; convergence order Crank–Nicolson scheme; weighted Shifted Grünwald–Letnikov approximation; space fractional convection-diffusion model; stability analysis; convergence order
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MDPI and ACS Style

Anley, E.F.; Zheng, Z. Finite Difference Method for Two-Sided Two Dimensional Space Fractional Convection-Diffusion Problem with Source Term. Mathematics 2020, 8, 1878. https://doi.org/10.3390/math8111878

AMA Style

Anley EF, Zheng Z. Finite Difference Method for Two-Sided Two Dimensional Space Fractional Convection-Diffusion Problem with Source Term. Mathematics. 2020; 8(11):1878. https://doi.org/10.3390/math8111878

Chicago/Turabian Style

Anley, Eyaya F.; Zheng, Zhoushun. 2020. "Finite Difference Method for Two-Sided Two Dimensional Space Fractional Convection-Diffusion Problem with Source Term" Mathematics 8, no. 11: 1878. https://doi.org/10.3390/math8111878

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