On the nonlinear stability of symplectic integrators

DOI10.1023/B:BITN.0000025088.13092.7fzbMath1070.65130OpenAlexW2099535332MaRDI QIDQ1826452

Matthew Perlmutter, Robert I. Mclachlan, Gilles Reinout Willem Quispel

Publication date: 6 August 2004

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/b:bitn.0000025088.13092.7f

zbMATH Keywords

Hamiltoniannonlinear stabilityRunge-Kutta methodsplitting methodssymplectic integrationbackward error analysis

Mathematics Subject Classification ID

Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for numerical methods for ordinary differential equations (65L70) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15) Numerical nonlinear stabilities in dynamical systems (65P40) Critical points of functions and mappings on manifolds (58K05) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25)

Related Items (3)

NONSTANDARD DISCRETIZATION SCHEMES APPLIED TO THE CONSERVATIVE HÉNON–HEILES SYSTEM ⋮ Preservation of stability properties near fixed points of linear Hamiltonian systems by symplectic integrators ⋮ Travelling wave solutions of multisymplectic discretizations of semi-linear wave equations

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