Higher-order averaging, formal series and numerical integration. II: The quasi-periodic case

DOI10.1007/s10208-012-9118-8zbMath1257.34031OpenAlexW2011378962MaRDI QIDQ695631

Ander Murua, Jesús María Sanz-Serna, Philippe Chartier

Publication date: 21 December 2012

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://hal.inria.fr/hal-00750601/file/cmss11-33.pdf

zbMATH Keywords

Lie groupsLie algebrastreesfirst integralsaveragingformal seriesB-seriesHamiltonian problemshighly oscillatory problemshigh-order averagingquasi-stroboscopic averagingnear-integrable systems

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) Hamilton's equations (70H05) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Explicit solutions, first integrals of ordinary differential equations (34A05) Averaging method for ordinary differential equations (34C29) Multifrequency systems of ordinary differential equations (34C46)

Related Items (16)

Computing normal forms and formal invariants of dynamical systems by means of word series ⋮ Word series for dynamical systems and their numerical integrators ⋮ A formal series approach to the center manifold theorem ⋮ Highly-oscillatory evolution equations with multiple frequencies: averaging and numerics ⋮ Word combinatorics for stochastic differential equations: splitting integrators ⋮ Vibrational resonance: a study with high-order word-series averaging ⋮ Asymptotic solvers for ordinary differential equations with multiple frequencies ⋮ Word series high-order averaging of highly oscillatory differential equations with delay ⋮ Averaging of highly-oscillatory transport equations ⋮ Highly Oscillatory Problems with Time-Dependent Vanishing Frequency ⋮ The Lie group structure of the Butcher group ⋮ Asymptotic stability estimates near an equilibrium point ⋮ A new class of uniformly accurate numerical schemes for highly oscillatory evolution equations ⋮ High-order stroboscopic averaging methods for highly oscillatory delay problems ⋮ A Technique for Studying Strong and Weak Local Errors of Splitting Stochastic Integrators ⋮ Higher-order averaging, formal series and numerical integration. III: Error bounds

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