Naslov
A general framework for conservative single-step time-integration schemes with higher-order accuracy for a central-force system

Autori
Graham, E. ; Jelenić, Gordan

Izvornik
Computer Methods in Applied Mechanics and Engineering (0045-7825) 192 (2003), 33-34; 3585-3618

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
conservative integration; central force field

Sažetak
A general framework for algorithms that conserve angular momentum for single-body central-force problems is presented. It is shown that any family of momentum-conserving algorithms can have at most three free parameters, one of which may be used to ensure energy conservation (and hence will be configuration-dependent). Further restrictions can be made that enable the algorithms to recover the orbits of relative equilibria of the underlying physical problem. In addition, the algorithms can be made time-reversible, whilst still leaving two parameters unspecified. The order of accuracy of a general momentum-conserving family is analysed, and it is shown that energy-momentum algorithms that preserve the underlying physical relative equilibria can have unlimited accuracy if the two remaining parameters are appropriately chosen functions of the configuration and the time-step: this does not require any additional degrees of freedom, extra stages of calculation or information from past solutions. Numerical examples are given that show the performance of some representative higher-order schemes when applied to stiff and non-stiff problems, and the issue of Newton-Raphson convergence is discussed.

Izvorni jezik
Engleski

Znanstvena područja
Temeljne tehničke znanosti

Napomena
Projekt EPSRC AF/100089

POVEZANOST RADA