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Geometric Numerical Integration
Structure-Preserving Algorithms for Ordinary Differential Equations
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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. This 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.
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Springer-Verlag Berlin and Heidelberg GmbH & Co. KG; May 2006
660 pages; ISBN 9783540306665
Read online, or download in secure PDF format
660 pages; ISBN 9783540306665
Read online, or download in secure PDF format
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3540306668
9783540306634
9783540306665