Diagonal implicit symplectic ERKN methods for solving oscillatory Hamiltonian systems

Mingxue Shi; Hao Zhang; Bin Wang

Diagonal implicit symplectic ERKN methods for solving oscillatory Hamiltonian systems

Numerical Analysis 2017-12-04 v1

Authors: Mingxue Shi , Hao Zhang , Bin Wang

Abstract

This paper studies diagonal implicit symplectic extended Runge--Kutta--Nystr\"{o}m (ERKN) methods for solving the oscillatory Hamiltonian system $H(q,p)=\dfrac{1}{2}p^{T}p+\dfrac{1}{2}q^{T}Mq+U(q)$ . Based on symplectic 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 and the numerical results demonstrate the remarkable numerical behavior of the new diagonal implicit symplectic methods when applied to the oscillatory Hamiltonian system.

Keywords

runge-kutta methods numerical analysis partial differential equations

Cite

@article{arxiv.1712.00296,
  title  = {Diagonal implicit symplectic ERKN methods for solving oscillatory Hamiltonian systems},
  author = {Mingxue Shi and Hao Zhang and Bin Wang},
  journal= {arXiv preprint arXiv:1712.00296},
  year   = {2017}
}

Comments

17 pages, 4 figures

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