Publication:
Higher-order averaging, formal series and numerical integration III: error bounds

Thumbnail Image
Identifiers
URI: https://hdl.handle.net/10016/32515
ISSN: 1615-3375
DOI: https://doi.org/10.1007/s10208-013-9175-7
UXXI: AR/0000020038
Files
higher-order_FCM_2015_ps.pdf (319.76 KB)
Publication date
2015-04-01
Defense date
Authors
Advisors
Tutors
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Impact
Google Scholar
Export
Research Projects
Organizational Units
Journal Issue
Abstract
In earlier papers, it has been shown how formal series like those used nowadays to investigate the properties of numerical integrators may be used to construct high-order averaged systems or formal first integrals of Hamiltonian problems. With the new approach the averaged system (or the formal first integral) may be written down immediately in terms of (i) suitable basis functions and (ii) scalar coefficients that are computed via simple recursions. Here we show how the coefficients/basis functions approach may be used advantageously to derive exponentially small error bounds for averaged systems and approximate first integrals.
Description
Keywords
Averaging, High-order averaging, Quasi-stroboscopic averaging, Highly oscillatory problems, Hamiltonian problems, Formal series, First integrals, Near-integrable systems
Bibliographic citation
Foundations of Computational Mathematics, (2015), v. 15, p.: 591–612..
Collections
DM - Artículos de Revistas