Stability and Convergence of an Implicit Difference Approximation for the Space Riesz Fractional Reaction-Dispersion Equation
Jinghua Chen 1*, Fawang Liu 21 College of Mathematics, Jimei University, Xiamen 361021, China
In this paper, we consider a Riesz space-fractional reaction-dispersion equation (RSFRDE). The RSFRDE is obtained from the classical reaction-dispersion equation by replacing the second-order space derivative with a Riesz derivative of order $\beta\in (1,2].$ We propose an implicit finite difference approximation for RSFRDE. The stability and convergence of the finite difference approximations are analyzed. Numerical results are found in good agreement with the theoretical analysis.
Key words: Riesz fractional derivative; fractional reaction-dispersion equation; implicit finite difference approximation; stability; convergence.
AMS subject classifications: 26A33, 35K57, 65M12