Conservative finite difference methods for fractional Schrodinger-Boussinesq equations and convergence analysis

被引：10
|
作者：
Liao, Feng [1 ]
Zhang, Luming [2 ]
Hu, Xiuling [3 ]
机构：
[1] Changshu Inst Technol, Sch Math & Stat, Changshu, Jiangsu, Peoples R China
[2] Nanjing Univ Aeronaut & Astronaut, Coll Sci, Nanjing, Jiangsu, Peoples R China
[3] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Jiangsu, Peoples R China
来源：
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2019年 / 35卷 / 04期
基金：
中国国家自然科学基金;
关键词：
conservative law; convergence; discrete energy method; mathematical induction method; Schrodinger-Boussinesq equations; GLOBAL WELL-POSEDNESS; NUMERICAL-ANALYSIS; ELEMENT-METHOD; SCHEME; SPACE; APPROXIMATION; EXISTENCE; BEHAVIOR;
D O I：
10.1002/num.22351
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, two conservative finite difference schemes for fractional Schrodinger-Boussinesq equations are formulated and investigated. The convergence of the nonlinear fully implicit scheme is established via discrete energy method, while the linear semi-implicit scheme is analyzed by means of mathematical induction method. Our schemes are proved to preserve the total mass and energy in discrete level. The numerical results are given to confirm the theoretical analysis.
引用
收藏
页码：1305 / 1325
页数：21
相关论文
共 50 条
  • [21] Dynamics of the discrete coupled nonlinear Schrodinger-Boussinesq equations
    Yang, Xinbo
    Zhao, Caidi
    Cao, Juan
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2013, 219 (16) : 8508 - 8524
  • [22] Conservative finite difference methods for the Boussinesq paradigm equation
    Xie, Jianqiang
    Wang, Quanxiang
    Zhang, Zhiyue
    [J]. MATHEMATICS AND COMPUTERS IN SIMULATION, 2023, 206 : 588 - 613
  • [23] Global well-posedness for the fractional Schrodinger-Boussinesq system
    Han, Lijia
    Zhang, Jingjun
    Guo, Boling
    [J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2014, 19 (08) : 2644 - 2652
  • [24] Multi-symplectic scheme for the coupled Schrodinger-Boussinesq equations
    Huang Lang-Yang
    Jiao Yan-Dong
    Liang De-Min
    [J]. CHINESE PHYSICS B, 2013, 22 (07)
  • [25] Application of the modified Kudryashov method to the generalized Schrodinger-Boussinesq equations
    Kumar, Dipankar
    Kaplan, Melike
    [J]. OPTICAL AND QUANTUM ELECTRONICS, 2018, 50 (09)
  • [26] An energy conservative difference scheme for the nonlinear fractional Schrodinger equations
    Wang, Pengde
    Huang, Chengming
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2015, 293 : 238 - 251
  • [27] The quadratic B-spline finite-element method for the coupled Schrodinger-Boussinesq equations
    Bai, Dongmei
    Zhang, Luming
    [J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2011, 88 (08) : 1714 - 1729
  • [28] Efficient energy-preserving methods for the Schrodinger-Boussinesq equation
    Yan, Jinliang
    Zheng, Lianghong
    Lu, Fuqiang
    Zhang, Qiongyue
    [J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2022,
  • [29] On the convergence and stability analysis of finite-difference methods for the fractional Newell-Whitehead-Segel equations
    Cilingir Sungu, Inci
    Aydin, Emre
    [J]. TURKISH JOURNAL OF MATHEMATICS, 2022, 46 (07) : 2806 - 2818
  • [30] Normal form analysis and chaotic scenario in a Schrodinger-Boussinesq system
    Saha, P
    Banerjee, S
    Chowdhury, AR
    [J]. CHAOS SOLITONS & FRACTALS, 2002, 14 (01) : 145 - 153
12345