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
收藏
页码：14 / 28
页数：15
相关论文
共 50 条
  • [1] Analysis of an Implicit Fully Discrete Local Discontinuous Galerkin Method for the Time-Fractional Kdv Equation
    Wei, Leilei
    He, Yinnian
    Zhang, Xindong
    ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2015, 7 (04) : 510 - 527
  • [2] Analysis of an implicit fully discrete local discontinuous Galerkin method for the time-fractional Schrodinger equation
    Wei, Leilei
    He, Yinnian
    Zhang, Xindong
    Wang, Shaoli
    FINITE ELEMENTS IN ANALYSIS AND DESIGN, 2012, 59 : 28 - 34
  • [3] NUMERICAL ANALYSIS OF THE FRACTIONAL SEVENTH-ORDER KDV EQUATION USING AN IMPLICIT FULLY DISCRETE LOCAL DISCONTINUOUS GALERKIN METHOD
    Wei, Leilei
    He, Yinnian
    Zhang, Yan
    INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2013, 10 (02) : 430 - 444
  • [4] A numerical study based on an implicit fully discrete local discontinuous Galerkin method for the time-fractional coupled Schrodinger system
    Wei, Leilei
    Zhang, Xindong
    Kumar, Sunil
    Yildirim, Ahmet
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2012, 64 (08) : 2603 - 2615
  • [5] Numerical Analysis of an Implicit Fully Discrete Local Discontinuous Galerkin Method for the Fractional Zakharoy-Kuznetsoy Equation
    Ren, Zongxiu
    Wei, Leilei
    He, Yinnian
    Wang, Shaoli
    MATHEMATICAL MODELLING AND ANALYSIS, 2012, 17 (04) : 558 - 570
  • [6] Analysis of the fractional Kawahara equation using an implicit fully discrete local discontinuous Galerkin method
    Wei, Leilei
    He, Yinnian
    Tang, Bo
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2013, 29 (05) : 1441 - 1458
  • [7] An Ultra-weak Local Discontinuous Galerkin Method with Generalized Numerical Fluxes for the KdV-Burgers-Kuramoto Equation
    Lin, Guotao
    Zhang, Dazhi
    Li, Jia
    Wu, Boying
    JOURNAL OF SCIENTIFIC COMPUTING, 2024, 99 (03)
  • [8] A Local Discontinuous Galerkin Method for Time-Fractional Burgers Equations
    Yuan, Wenping
    Chen, Yanping
    Huang, Yunqing
    EAST ASIAN JOURNAL ON APPLIED MATHEMATICS, 2020, 10 (04) : 818 - 837
  • [9] Numerical algorithm based on an implicit fully discrete local discontinuous Galerkin method for the fractional diffusion-wave equation
    Huiya Dai
    Leilei Wei
    Xindong Zhang
    Numerical Algorithms, 2014, 67 : 845 - 862
  • [10] Numerical algorithm based on an implicit fully discrete local discontinuous Galerkin method for the fractional diffusion-wave equation
    Dai, Huiya
    Wei, Leilei
    Zhang, Xindong
    NUMERICAL ALGORITHMS, 2014, 67 (04) : 845 - 862
12345