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
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
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页码:430 / 444
页数:15
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