NUMERICAL ANALYSIS OF THE FRACTIONAL SEVENTH-ORDER KDV EQUATION USING AN IMPLICIT FULLY DISCRETE LOCAL DISCONTINUOUS GALERKIN METHOD

被引：0

作者：

Wei, Leilei ^{[1
]}

He, Yinnian ^{[1
]}

Zhang, Yan ^{[2
]}

机构：

[1] Xi An Jiao Tong Univ, Sch Math & Stat, Ctr Computat Geosci, Xian 710049, Peoples R China

[2] Univ Paris 06, UMR 7598, CNRS, Lab Jacques Louis Lions, F-75005 Paris, France

来源：

INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING | 2013年 / 10卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Time-fractional partial differential equations; Seventh-order KdV equation; Local discontinuous Galerkin method; Stability; Error estimates; HOMOTOPY PERTURBATION METHOD; FINITE-ELEMENT-METHOD; SCHRODINGER-EQUATION; DIFFUSION EQUATION; WAVE SOLUTIONS; SPACE;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper an implicit fully discrete local discontinuous Galerkin (LDG) finite element method is applied to solve the time-fractional seventh-order Korteweg-de Vries (sKdV) equation, which is introduced by replacing the integer-order time derivatives with fractional derivatives. We prove that our scheme is unconditional stable and L-2 error estimate for the linear case with the convergence rate O(h(k+1) + (Delta t)(2) + (Delta t)(alpha/2) h(k+1/2)) through analysis. Extensive numerical results are provided to demonstrate the performance of the present method.

引用

页码：430 / 444

页数：15

共 27 条

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