Efficient Energy-preserving Methods for General Nonlinear Oscillatory Hamiltonian System

被引：0

作者：

Yong Lei FANG ^{[1
]}

Chang Ying LIU ^{[2
]}

Bin WANG ^{[3
]}

机构：

[1] School of Mathematics and Statistics, Zaozhuang University

[2] School of Mathematics and Statistics, Nanjing University of Information Science & Technology

[3] School of Mathematical Sciences, Qufu Normal University

来源：

ActaMathematicaSinica | 2018年 / 34卷 / 12期

关键词：

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

In this paper, we propose and analyze two kinds of novel and symmetric energy-preserving formulae for the nonlinear oscillatory Hamiltonian system of second-order differential equations Aq''（t）+Bq（t） = f(q（t）), where A ∈ Rm×m is a symmetric positive definite matrix, B ∈ Rm×m is a symmetric positive semi-definite matrix that implicitly contains the main frequencies of the problem and f（q） =-▽q V（q） for a real-valued function V（q）. The energy-preserving formulae can exactly preserve the Hamiltonian H（q', q） =12 q'TAq' +12 qTBq + V（q）. We analyze the properties of energy-preserving and convergence of the derived energy-preserving formula and obtain new efficient energy-preserving integrators for practical computation. Numerical experiments are carried out to show the efficiency of the new methods by the nonlinear Hamiltonian systems.

引用

页码：1863 / 1878

页数：16

共 21 条

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