Geometric numerical integration : structure-preserving algorithms for ordinary differential equations
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, com...
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| Auteurs principaux: | , , |
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| Format: | Livre numérique |
| Sprog: | Anglais |
| Udgivet: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Udgivelse: | 2nd edition. |
| Serier: | Springer Series in Computational Mathematics
31 |
| Fag: | |
| Online adgang: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Kommentar: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Geometric numerical integration, structure-preserving algorithms for ordinary differential equations, Ernst Hairer, Christian Lubich, Gerhard Wanner, 2nd edition, 2006, Berlin, Springer, 1 volume (xvii-644 pages), Springer series in computational mathematics, 978-3-540-30663-4 • Geometric Numerical Integration, Texte imprimé, 9783540818328 • Geometric numerical integration, structure-preserving algorithms for ordinary differential equations, Ernst Hairer, Christian Lubich, Gerhard Wanner, 2nd edition, 2006, Berlin, Springer, 1 volume (xvii-644 pages), Springer series in computational mathematics, 978-3-540-30663-4 • Geometric Numerical Integration, Texte imprimé, 9783642051579 |
| Summary: | 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 |
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| Emne beskrivelse: | Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Bibliografi: | Bibliogr. p. [617]-636 de l'édition imprimée. Notes bibliogr. Index |
| ISBN: | 9783540306665 |
| ISSN: | 2198-3712 |
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