Author(s)

Dechao Gao, Zeshan Qiu^*, Lizan Wang, Jianxin Li

Department of Basic Education, Xinjiang University of Political Science and Law, Tumushuke, China.

The higher-order numerical scheme of nonlinear advection-diffusion equations is studied in this article, where the space fractional derivatives are evaluated by using weighted and shifted Grünwald difference operators and combining the compact technique, in the time direction is discretized by the Crank-Nicolson method. Through the energy method, the stability and convergence of the numerical scheme in the sense of L₂-norm are proved, and the convergence order is . Some examples are given to show that our numerical scheme is effective.

Crank-Nicolson Quasi-Compact Scheme, Fractional Advection-Diffusion Equations, Nonlinear, Stability and Convergence

Gao, D. , Qiu, Z. , Wang, L. and Li, J. (2024) Crank-Nicolson Quasi-Compact Scheme for the Nonlinear Two-Sided Spatial Fractional Advection-Diffusion Equations. Journal of Applied Mathematics and Physics, 12, 1089-1100. doi: 10.4236/jamp.2024.124068.