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

页码：1305 / 1325

页数：21

共 50 条

[1] Unconditional L∞ convergence of a conservative compact finite difference scheme for the N-coupled Schrodinger-Boussinesq equations
Liao, Feng
Zhang, Luming
Wang, Tingchun
[J]. APPLIED NUMERICAL MATHEMATICS, 2019, 138 : 54 - 77
[2] Efficient and conservative compact difference scheme for the coupled Schrodinger-Boussinesq equations
He, Yuyu
Chen, Hongtao
[J]. APPLIED NUMERICAL MATHEMATICS, 2022, 182 : 285 - 307
[3] Conservative Compact Finite Difference Scheme for the Coupled Schrodinger-Boussinesq Equation
Liao, Feng
Zhang, Luming
[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2016, 32 (06) : 1667 - 1688
[4] Numerical analysis of a conservative linear compact difference scheme for the coupled Schrodinger-Boussinesq equations
Liao, Feng
Zhang, Luming
[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2018, 95 (05) : 961 - 978
[5] Numerical analysis for a conservative difference scheme to solve the Schrodinger-Boussinesq equation
Zhang, Luming
Bai, Dongmei
Wang, Shanshan
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (17) : 4899 - 4915
[6] Analysis of the linearly energy- and mass-preserving finite difference methods for the coupled Schrodinger-Boussinesq equations
Deng, Dingwen
Wu, Qiang
[J]. APPLIED NUMERICAL MATHEMATICS, 2021, 170 : 14 - 38
[7] ON SCHRODINGER-BOUSSINESQ EQUATIONS
Linares, F.
Navas, A.
[J]. ADVANCES IN DIFFERENTIAL EQUATIONS, 2004, 9 (1-2) : 159 - 176
[8] Linearized and decoupled structure-preserving finite difference methods and their analyses for the coupled Schrodinger-Boussinesq equations
Deng, Dingwen
Wu, Qiang
[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2021, 37 (05) : 2924 - 2951
[9] Conservative Fourier spectral scheme for the coupled Schrodinger-Boussinesq equations
Wang, Junjie
[J]. ADVANCES IN DIFFERENCE EQUATIONS, 2018,
[10] Finite dimensional global attractor for dissipative Schrodinger-Boussinesq equations
Li, YS
Chen, QY
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1997, 205 (01) : 107 - 132

← 1 2 3 4 5 →