Numerical algorithm based on an implicit fully discrete local discontinuous Galerkin method for the time-fractional KdV-Burgers-Kuramoto equation

被引：19

作者：

Wei, Leilei ^{[1
]}

He, Yinnian ^{[1
]}

Yildirim, Ahmet ^{[2
]}

Kumar, Sunil ^{[3
]}

机构：

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

[2] Ege Univ, Fac Sci, Dept Math, TR-351000 Bornova, Turkey

[3] Natl Inst Technol, Dept Math, Jamshedpur 831014, Jharkhand, India

来源：

ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK | 2013年 / 93卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Time-fractional partial differential equations; KdV-Burgers-Kuramoto equation; local discontinuous Galerkin method; stability; error estimates; HOMOTOPY PERTURBATION METHOD; PETROVSKII-PISKUNOV EQUATION; FINITE-ELEMENT-METHOD; DIFFERENTIAL-EQUATIONS; DIFFUSION EQUATION; WAVE-EQUATIONS; CONVECTION; TERM;

D O I：

10.1002/zamm.201200003

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 considered for solving the time-fractional KdV-Burgers-Kuramoto (KBK) equation. The scheme is based on a finite difference method in time and local discontinuous Galerkin methods in space. We prove that our scheme is unconditional stable and L2 error estimate for the linear case with the convergence rate O(hk+1 + (Delta t)2+ (Delta t)alpha/2hk+1/2). Numerical examples are presented to show the efficiency and accuracy of our scheme.

引用

页码：14 / 28

页数：15

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