Spectral variational integrators for semi-discrete Hamiltonian wave equations

被引：5

作者：

Li, Yiqun ^{[1
]}

Wu, Boying ^{[1
]}

Leok, Melvin ^{[2
]}

机构：

[1] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China

[2] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2017年 / 325卷

基金：

中国国家自然科学基金; 美国国家科学基金会;

关键词：

Hamiltonian PDEs; Spectral variational integrator; Semi-discrete; Symmetric difference; MULTI-SYMPLECTIC INTEGRATORS; NUMERICAL-SOLUTION; SCHEMES; PDES; SYSTEMS;

D O I：

10.1016/j.cam.2017.04.043

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present a highly accurate Hamiltonian structure-preserving numerical method for simulating Hamiltonian wave equations. This method is obtained by applying spectral variational integrators (SVI) to the system of Hamiltonian ODEs which are derived from the spatial semi-discretization of the Hamiltonian PDE. The spatial variable is discretized by using high-order symmetric finite-differences. An efficient implementation of SVI for high-dimensional systems of ODEs is presented. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：56 / 73

页数：18

共 50 条

[1] Some applications of semi-discrete variational integrators to classical field theories
de Leòn M.
Marrero J.C.
de Diego D.M.
[J]. Qualitative Theory of Dynamical Systems, 2008, 7 (1) : 195 - 212
[2] Discrete Hamiltonian variational integrators
Leok, Melvin
Zhang, Jingjing
[J]. IMA JOURNAL OF NUMERICAL ANALYSIS, 2011, 31 (04) : 1497 - 1532
[3] Stochastic discrete Hamiltonian variational integrators
Holm, Darryl D.
Tyranowski, Tomasz M.
[J]. BIT NUMERICAL MATHEMATICS, 2018, 58 (04) : 1009 - 1048
[4] Stochastic discrete Hamiltonian variational integrators
Darryl D. Holm
Tomasz M. Tyranowski
[J]. BIT Numerical Mathematics, 2018, 58 : 1009 - 1048
[5] INDIRECT BOUNDARY OBSERVABILITY OF SEMI-DISCRETE COUPLED WAVE EQUATIONS
El Akri, Abdeladim
Maniar, Lahcen
[J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2018,
[6] Discrete Hamiltonian Variational Mechanics and Hamel’s Integrators
Shan Gao
Donghua Shi
Dmitry V. Zenkov
[J]. Journal of Nonlinear Science, 2023, 33
[7] Algebraic entropy for semi-discrete equations
Demskoi, D. K.
Viallet, C-M
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2012, 45 (35)
[8] Discrete doubly periodic and solitary wave solutions for the semi-discrete coupled mKdV equations
Wu Xiao-Fei
Zhu Jia-Min
Ma Zheng-Yi
[J]. CHINESE PHYSICS, 2007, 16 (08): : 2159 - 2166
[9] A semi-discrete numerical method for convolution-type unidirectional wave equations
Erbay, H. A.
Erbay, S.
Erkip, A.
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2021, 387
[10] On the energy estimates of semi-discrete wave equations with time dependent propagation speed
Hirosawa, Fumihiko
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021, 496 (01)

← 1 2 3 4 5 →