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

Eyaya Fekadie Anley and Zhoushun Zheng
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Eyaya Fekadie Anley: School of Mathematics and Statistics, Central South University, Changsha 410083, China
Zhoushun Zheng: School of Mathematics and Statistics, Central South University, Changsha 410083, China

Mathematics, 2020, vol. 8, issue 11, 1-27

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.

Keywords: Crank–Nicolson scheme; weighted Shifted Grünwald–Letnikov approximation; space fractional convection-diffusion model; stability analysis; convergence order (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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