Error growth in the numerical integration of periodic orbits

DOI10.1016/j.matcom.2011.05.007zbMath1231.65129OpenAlexW1967685344MaRDI QIDQ654360

Manuel Calvo, M. P. Laburta, Luis Rández, Juan I. Montijano

Publication date: 28 December 2011

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2011.05.007

zbMATH Keywords

numerical examplesRunge-Kutta methodsgeometric integrationvariable step sizelong-time integrationperiodic flowserror growthinvariant preservationone step methods

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for numerical methods for ordinary differential equations (65L70) Periodic and quasi-periodic flows and diffeomorphisms (37C55)

Related Items (7)

Multiple-relaxation Runge Kutta methods for conservative dynamical systems ⋮ Energy-preserving methods for Poisson systems ⋮ Line integral methods which preserve all invariants of conservative problems ⋮ Multiple invariants conserving Runge-Kutta type methods for Hamiltonian problems ⋮ On the rate of error growth in time for numerical solutions of nonlinear dispersive wave equations ⋮ Relaxation Runge-Kutta methods for Hamiltonian problems ⋮ Unnamed Item

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