ERROR ANALYSIS OF DISCONTINUOUS GALERKIN METHOD FOR THE TIME FRACTIONAL KDV EQUATION WITH WEAK SINGULARITY SOLUTION

被引：14
|
作者：
An, Na [1 ]
Huang, Chaobao [2 ]
Yu, Xijun [3 ]
机构：
[1] Shandong Normal Univ, Sch Math & Stat, Jinan 250014, Shandong, Peoples R China
[2] Shandong Univ Finance & Econ, Sch Math & Quantitat Econ, Jinan 250014, Shandong, Peoples R China
[3] Inst Appl Phys & Computat Math, Lab Computat Phys, Beijing 100088, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2020年 / 25卷 / 01期
关键词：
Time fractional KdV equation; weak singularity; discontinuous Galerkin method; stability; error estimate; TERM;
D O I：
10.3934/dcdsb.2019185
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this work, the time fractional KdV equation with Caputo time derivative of order alpha is an element of (0, 1) is considered. The solution of this problem has a weak singularity near the initial time t = 0. A fully discrete discontinuous Galerkin (DG) method combining the well-known L1 discretisation in time and DG method in space is proposed to approximate the time fractional KdV equation. The unconditional stability result and O(N--min{r alpha,N-2-alpha}+ h(k+1)) convergence result for P-k (k >= 2) polynomials are obtained. Finally, numerical experiments are presented to illustrate the efficiency and the high order accuracy of the proposed scheme.
引用
收藏
页码：321 / 334
页数：14
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