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Liu, F., Zhuang, P. and Burrage, K. (2012) Numerical Methods and Analysis for a Class of Fractional Advection-Dispersion Models. Computers & Mathematics with Applications, 64, 2990-3007.
https://doi.org/10.1016/j.camwa.2012.01.020

has been cited by the following article:

• TITLE: Crank-Nicolson Quasi-Compact Scheme for the Nonlinear Two-Sided Spatial Fractional Advection-Diffusion Equations

  AUTHORS: Dechao Gao, Zeshan Qiu, Lizan Wang, Jianxin Li

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

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.12 No.4, April 19, 2024

  ABSTRACT: 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.