RT Journal Article
T1 Higher-order averaging, formal series and numerical integration III: error bounds
A1 Chartier, P.
A1 Murua, A.
A1 Sanz Serna, Jesús María
AB 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.
PB Springer
SN 1615-3375
YR 2015
FD 2015-04-01
LK https://hdl.handle.net/10016/32515
UL https://hdl.handle.net/10016/32515
LA eng
NO A. Murua and J.M. Sanz-Serna have been supported by projects MTM2010-18246-C03-03 and MTM2010-18246-C03-01 respectively from Ministerio de Ciencia e Innovación.
DS e-Archivo
RD 1 sept. 2024