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Diagonal implicit symplectic extended RKN methods for solving oscillatory Hamiltonian systems

  • Mingxue Shi
  • Hao Zhang
  • Bin WangEmail author
Article
  • 23 Downloads

Abstract

This paper studies diagonal implicit symplectic extended Runge–Kutta–Nyström (ERKN) methods for solving the oscillatory Hamiltonian system \(H(q,p)=\dfrac{1}{2}p^\mathrm{T}p+\dfrac{1}{2}q^\mathrm{T}Mq+U(q)\). 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.

Keywords

Diagonal implicit methods Symplectic methods ERKN methods Oscillatory Hamiltonian systems 

Mathematics Subject Classification

65L05 65L20 65P10 

Notes

Acknowledgements

The authors are sincerely thankful to two anonymous reviewers for their valuable suggestions, which help improve the presentation of the manuscript significantly.

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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesQufu Normal UniversityQufuChina

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