TITLE:
Local Discontinuous Galerkin Method for the Time-Fractional KdV Equation with the Caputo-Fabrizio Fractional Derivative
AUTHORS:
Huanhuan Wang, Xiaoyan Xu, Junmei Dou, Ting Zhang, Leilei Wei
KEYWORDS:
Caputo-Fabrizio Fractional Derivative, Local Discontinuous Galerkin Method, Stability, Error Analysis
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.6,
June
24,
2022
ABSTRACT: This paper studies the time-fractional Korteweg-de Vries (KdV) equations with Caputo-Fabrizio fractional derivatives. The scheme is presented by using a finite difference method in temporal variable and a local discontinuous Galerkin method (LDG) in space. Stability and convergence are demonstrated by a specific choice of numerical fluxes. Finally, the efficiency and accuracy of the scheme are verified by numerical experiments.