A new high precision energy-preserving integrator for system of oscillatory second-order differential equations

被引：54

作者：

Wang, Bin ^{[1
]}

Wu, Xinyuan ^{[1
]}

机构：

[1] Nanjing Univ, Dept Math, State Key Lab Novel Software Technol, Nanjing 210093, Jiangsu, Peoples R China

来源：

PHYSICS LETTERS A | 2012年 / 376卷 / 14期

关键词：

Hamiltonian systems; Energy-preserving integrators; Oscillatory differential equations; Fermi-Pasta-Ulam problem; NUMERICAL-METHODS; CONSERVATION; SCHEMES;

D O I：

10.1016/j.physleta.2012.02.040

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

This Letter proposes a new high precision energy-preserving integrator for system of oscillatory second-order differential equations q ''(t) + Mq(t) = f(q(t)) with a symmetric and positive semi-definite matrix M and f(q) = -del U(q). The system is equivalent to a separable Hamiltonian system with Hamiltonian H(p, q) = 1/2 p(T) p + 1/2 q(T) Mq + U(q). The properties of the new energy-preserving integrator are analyzed. The well-known Fermi-Pasta-Ulam problem is performed numerically to show that the new integrator preserves the energy integral with higher accuracy than Average Vector Field (AVF) method and an energy-preserving collocation method. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：1185 / 1190

页数：6

共 37 条

[1]

[Anonymous], 1955, Los Alamos Report

[2]

Brugnano L., 2010, JNAIAM J NUMER ANAL, V5, P17

[3]

Celledoni E., 2010, JNAIAM J NUMER ANAL, V5, P85

[4] Energy-Preserving Integrators and the Structure of B-series [J].