Runge-Kutta method, finite element method, and regular algorithms for Hamiltonian system

被引：4

作者：

胡妹芳 ^{[1
,2
]}

陈传淼 ^{[1
]}

机构：

[1] College of Mathematics and Computer Science, Hunan Normal University

[2] Institute of Mathematics and Physics, Central South University of Forestry and Technology

来源：

Applied Mathematics and Mechanics(English Edition) | 2013年 / 34卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Hamiltonian system; energy conservation; symplecticity; finite element method; Runge-Kutta method;

D O I：

暂无

中图分类号：

O241.82 [偏微分方程的数值解法];

学科分类号：

070102 ;

摘要：

The symplectic algorithm and the energy conservation algorithm are two important kinds of algorithms to solve Hamiltonian systems. The symplectic Runge-Kutta (RK) method is an important part of the former, and the continuous finite element method (CFEM) belongs to the later. We find and prove the equivalence of one kind of the implicit RK method and the CFEM, give the coefficient table of the CFEM to simplify its computation, propose a new standard to measure algorithms for Hamiltonian systems, and define another class of algorithms-the regular method. Finally, numerical experiments are given to verify the theoretical results.

引用

页码：747 / 760

页数：14

共 50 条

[1] Runge-kutta method, finite element method, and regular algorithms for hamiltonian system
Hu, Shu-fang
Chen, Chuan-miao
APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION, 2013, 34 (06) : 747 - 760
[2] Runge-kutta method, finite element method, and regular algorithms for hamiltonian system
Shu-fang Hu
Chuan-miao Chen
Applied Mathematics and Mechanics, 2013, 34 : 747 - 760
[3] Integration method and Runge-Kutta method
Sanprasert, Wannaporn
Chundang, Ungsana
Podisuk, Maitree
PROCEEDINGS OF THE 15TH AMERICAN CONFERENCE ON APPLIED MATHEMATICS AND PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON COMPUTATIONAL AND INFORMATION SCIENCES 2009, VOLS I AND II, 2009, : 232 - +
[4] Runge-Kutta convolution quadrature for the Boundary Element Method
Banjai, Lehel
Messner, Matthias
Schanz, Martin
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2012, 245 : 90 - 101
[5] Runge-Kutta Finite Element Method Based on the Characteristic for the Incompressible Navier-Stokes Equations
Liao, Shaokai
Zhang, Yan
Chen, Da
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2019, 11 (06) : 1415 - 1435
[6] The Runge-Kutta DG finite element method and the KFVS scheme for compressible flow simulations
Yu, Xijun
Dai, Qingfang
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2006, 22 (06) : 1455 - 1478
[7] Symplectic Partitioned Runge-Kutta And Symplectic Runge-Kutta Methods Generated By 2-Stage RadauIA Method
Tan, Jiabo
ADVANCES IN COMPUTATIONAL MODELING AND SIMULATION, PTS 1 AND 2, 2014, 444-445 : 633 - 636
[8] A quasi-randomized Runge-Kutta method
Coulibaly, I
Lécot, C
MATHEMATICS OF COMPUTATION, 1999, 68 (226) : 651 - 659
[9] Runge-Kutta method with equation dependent coefficients
Ixaru, L. Gr.
COMPUTER PHYSICS COMMUNICATIONS, 2012, 183 (01) : 63 - 69
[10] Adversarial Attack Based on Runge-Kutta Method
Wan C.
Huang F.-J.
Ruan Jian Xue Bao/Journal of Software, 2024, 35 (05): : 2543 - 2565

← 1 2 3 4 5 →