Analysis of an Implicit Fully Discrete Local Discontinuous Galerkin Method for the Time-Fractional Kdv Equation
Year: 2015
Author: Leilei Wei, Yinnian He, Xindong Zhang
Advances in Applied Mathematics and Mechanics, Vol. 7 (2015), Iss. 4 : pp. 510–527
Abstract
In this paper, we consider a fully discrete local discontinuous Galerkin (LDG) finite element method for a time-fractional Korteweg-de Vries (KdV) equation. The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space. We show that our scheme is unconditionally stable and convergent through analysis. Numerical examples are shown to illustrate the efficiency and accuracy of our scheme.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2013.m220
Advances in Applied Mathematics and Mechanics, Vol. 7 (2015), Iss. 4 : pp. 510–527
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Author Details
-
A Petrov–Galerkin spectral method for the linearized time fractional KdV equation
Chen, Hu | Sun, TaoInternational Journal of Computer Mathematics, Vol. 95 (2018), Iss. 6-7 P.1292
https://doi.org/10.1080/00207160.2017.1410544 [Citations: 11] -
Hamiltonian Boundary Value Method for the Nonlinear Schrödinger Equation and the Korteweg-de Vries Equation
Song, Mingzhan | Qian, Xu | Zhang, Hong | Song, SongheAdvances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 4 P.868
https://doi.org/10.4208/aamm.2015.m1356 [Citations: 9] -
Second order difference schemes for time-fractional KdV–Burgers’ equation with initial singularity
Cen, Dakang | Wang, Zhibo | Mo, YanApplied Mathematics Letters, Vol. 112 (2021), Iss. P.106829
https://doi.org/10.1016/j.aml.2020.106829 [Citations: 37] -
Local error estimate of L1 scheme for linearized time fractional KdV equation with weakly singular solutions
Chen, Hu | Chen, Mengyi | Sun, Tao | Tang, YifaApplied Numerical Mathematics, Vol. 179 (2022), Iss. P.183
https://doi.org/10.1016/j.apnum.2022.04.021 [Citations: 5] -
A finite difference scheme on graded meshes for time-fractional nonlinear Korteweg-de Vries equation
Shen, Jinye | Sun, Zhi-zhong | Cao, WanrongApplied Mathematics and Computation, Vol. 361 (2019), Iss. P.752
https://doi.org/10.1016/j.amc.2019.06.023 [Citations: 13] -
Effective numerical simulation of time fractional KdV equation with weakly singular solutions
Chen, Hu | Lin, Xiaotang | Sun, Tao | Tang, Yifa | Zhang, JingnaInternational Journal of Modeling, Simulation, and Scientific Computing, Vol. 15 (2024), Iss. 03
https://doi.org/10.1142/S179396232450020X [Citations: 0] -
High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments
Shu, Chi-Wang
Journal of Computational Physics, Vol. 316 (2016), Iss. P.598
https://doi.org/10.1016/j.jcp.2016.04.030 [Citations: 126] -
L1 scheme on graded mesh for the linearized time fractional KdV equation with initial singularity
Chen, Hu | Hu, Xiaohan | Ren, Jincheng | Sun, Tao | Tang, YifaInternational Journal of Modeling, Simulation, and Scientific Computing, Vol. 10 (2019), Iss. 01 P.1941006
https://doi.org/10.1142/S179396231941006X [Citations: 11] -
Fast L2-1σ Galerkin FEMs for generalized nonlinear coupled Schrödinger equations with Caputo derivatives
Li, Meng | Wei, Yifan | Niu, Binqian | Zhao, Yong-LiangApplied Mathematics and Computation, Vol. 416 (2022), Iss. P.126734
https://doi.org/10.1016/j.amc.2021.126734 [Citations: 3]