An efficient difference scheme for time-fractional KdV equation

被引：5
|
作者：
Xing, Zhiyong [1 ,2 ]
Wen, Liping [3 ]
Wang, Wansheng [1 ]
机构：
[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China
[2] Shaoyang Univ, Dept Math, Shaoyang 422000, Hunan, Peoples R China
[3] Xiangtan Univ, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Hunan, Peoples R China
来源：
COMPUTATIONAL & APPLIED MATHEMATICS | 2021年 / 40卷 / 08期
基金：
上海市自然科学基金;
关键词：
Time-fractional KdV equation; Caputo fractional derivative; L2-1(sigma) method; Weak singularity; Grade mesh; GRADED MESHES;
D O I：
10.1007/s40314-021-01657-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, an efficient numerical method is proposed for the nonlinear time fractional Korteweg-de Vries (KdV) equation with Caputo fractional derivative of order alpha is an element of (0, 1). The scheme is based on a nonuniform L2-1(sigma) formula in time and a second-order finite difference in space. The numerical method can not only effectively deal with the weak singularity of the fractional model at t = 0, but also has high accuracy. The stability and convergence of the difference scheme are rigorously established. Finally, several numerical experiments are provided to support the theoretical results.
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页数：20
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