Error Growth in the Numerical Integration of Periodic Orbits, with Application to Hamiltonian and Reversible Systems

DOI10.1137/S0036142995281152zbMath0889.65081OpenAlexW2015331834MaRDI QIDQ4377513

Begoña Cano, Jesús María Sanz-Serna

Publication date: 10 February 1998

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0036142995281152

zbMATH Keywords

periodic solutionsperiodic orbitsconservation of energyreversible systemsHamiltonian systemsRunge-Kutta methodssymplectic integratorserror growthasymptotic expansion of the errorvariable stepsizes

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Hamilton's equations (70H05) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Error bounds for numerical methods for ordinary differential equations (65L70) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

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