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Article
Geometric numerical integration illustrated by the Stoermer-Verlet
method
HAIRER, Ernst, LUBICH, Christian, WANNER, Gerhard
Abstract
The subject of geometric numerical integration deals with numerical integrators that preserve
geometric properties of the flow of a differential equation, and it explains how structure
preservation leads to an improved long-time behaviour. This article illustrates concepts and
results of geometric numerical integration on the important example of the Störmer/Verlet
method. It thus presents a cross-section of the recent monograph by the authors, enriched by
some additional material. After an introduction to the Newton-Störmer-Verlet-leapfrog method
and its various interpretations, there follows a discussion of geometric properties: reversibility,
symplecticity, volume preservation, and conservation of first integrals. The extension to
Hamiltonian systems on manifolds is also described. The theoretical foundation relies on a
backward error analysis, which translates the geometric properties of the method into the
structure of a modified differential equation, whose flow is nearly identical to the numerical
method. Combined with results from perturbation theory, this explains the excellent long-time
behaviour of the [...]
Reference
HAIRER, Ernst, LUBICH, Christian, WANNER, Gerhard. Geometric numerical integration
illustrated by the Stoermer-Verlet method. Acta Numerica, 2003, vol. 12, p. 399-450
DOI : 10.1017/S0962492902000144
Available at:
http://archive-ouverte.unige.ch/unige:12277
Disclaimer: layout of this document may differ from the published version.
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