Diagonal implicit symplectic extended RKN methods for solving oscillatory Hamiltonian systems

被引：0

作者：

Shi, Mingxue ^{[1
]}

Zhang, Hao ^{[1
]}

Wang, Bin ^{[1
]}

机构：

[1] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2019年 / 38卷 / 01期

关键词：

Diagonal implicit methods; Symplectic methods; ERKN methods; Oscillatory Hamiltonian systems; KUTTA-NYSTROM METHODS; FOURIER COLLOCATION METHODS; ENERGY-CONSERVATION; ERKN INTEGRATORS; IMPLEMENTATION;

D O I：

10.1007/s40314-019-0786-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper studies diagonal implicit symplectic extended Runge-Kutta-Nystrom (ERKN) methods for solving the oscillatory Hamiltonian system H(q,p)=1/2pTp+12qTMq+U(q). Based on symplecticity conditions and order conditions, we construct some diagonal implicit symplectic ERKN methods. The stability of the obtained methods is discussed. Three numerical experiments are carried out to show the performance of the methods. It follows from the numerical results that the new diagonal implicit symplectic methods are more effective than RKN methods when applied to the oscillatory Hamiltonian system.

引用

页数：17

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