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Analysis of an Implicit Fully Discrete Local Discontinuous Galerkin Method for the Time-Fractional Kdv Equation

Published online by Cambridge University Press:  29 May 2015

Leilei Wei ,
Yinnian He  and
Xindong Zhang
Leilei Wei
Affiliation:
College of Science, Henan University of Technology, Zhengzhou 450001, China
Yinnian He*
Affiliation:
Center for Computational Geosciences, School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
Xindong Zhang
Affiliation:
College of Mathematics Sciences, Xinjiang Normal University, Urumqi 830054, China
*
*Corresponding author. Email: leileiwei09@gmail.com (L. Wei), heyn@mail.xjtu.edu.cn (Y. He), liaoyuan1126@163.com (X. Zhang)
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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.

Keywords

65M6035K55Time-fractional partial differential equationsKdv equationlocal discontinuous Galerkin methodstabilityerror estimates
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 7 , Issue 4 , August 2015 , pp. 510 - 527
Copyright
Copyright © Global-Science Press 2015 

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