Numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions are the subject of this book. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book is illustrated by many figures, it treats applications from physics and astronomy and contains many numerical experiments and comparisons of different approaches. The second edition is substantially revised and enlarged, with many improvements in the presentation and additions concerning in particular non-canonical Hamiltonian systems, highly oscillatory mechanical systems, and the dynamics of multistep methods.
Springer Series in Computational Mathematics
Editorial Board R. Bank R.L. Graham J. Stoer R. Varga H. Yserentant
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Ernst Hairer Christian Lubich Gerhard Wanner
Geometric Numerical Integration Structure-Preserving Algorithms for Ordinary Differential Equations Second Edition
With 146 Figures
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Ernst Hairer Gerhard Wanner
Christian Lubich Mathematisches Institut Universität Tübingen Auf der Morgenstelle 10 72076 Tübingen, Germany email:
[email protected]
Section de Mathématiques Université de Genève 2-4 rue du Lièvre, C.P. 64 CH-1211 Genève 4, Switzerland email: