ERKN methods for long-term integration of multidimensional orbital problems

DOI10.1016/j.apm.2012.05.021zbMath1349.65233OpenAlexW1966078277MaRDI QIDQ346148

Kai Liu, Hua Zhao, Bin Wang, Xin-Yuan Wu

Publication date: 5 December 2016

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apm.2012.05.021

zbMATH Keywords

oscillatory systemsorbital problemsextended Runge-Kutta-Nyström methodsstructure preservation

Mathematics Subject Classification ID

Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Time series analysis of dynamical systems (37M10) Orbital mechanics (70M20) Dynamical systems in classical and celestial mechanics (37N05)

Related Items (12)

Sixth-order symplectic and symmetric explicit ERKN schemes for solving multi-frequency oscillatory nonlinear Hamiltonian equations ⋮ A simplified Nyström-tree theory for extended Runge-Kutta-Nyström integrators solving multi-frequency oscillatory systems ⋮ A Filon-type asymptotic approach to solving highly oscillatory second-order initial value problems ⋮ An improved tri-coloured rooted-tree theory and order conditions for ERKN methods for general multi-frequency oscillatory systems ⋮ A feasible and effective technique in constructing ERKN methods for multi-frequency multidimensional oscillators in scientific computation ⋮ The construction of arbitrary order ERKN methods based on group theory for solving oscillatory Hamiltonian systems with applications ⋮ Explicit multi-symplectic extended leap-frog methods for Hamiltonian wave equations ⋮ Error bounds for explicit ERKN integrators for systems of multi-frequency oscillatory second-order differential equations ⋮ An Essential Extension of the Finite-Energy Condition for Extended Runge-Kutta-Nyström Integrators when Applied to Nonlinear Wave Equations ⋮ Effective integrators for nonlinear second-order oscillatory systems with a time-dependent frequency matrix ⋮ The performance of the \(N\)-body integrator SSS ⋮ The tri-coloured free-tree theory for symplectic multi-frequency ERKN methods

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