Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2002
|
| Schriftenreihe: | Springer Series in Computational Mathematics
31 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The subject of this book is numerical methods that preserve geometric properties of the flow of a differential equation: symplectic integrators for Hamiltonian systems, symmetric integrators for reversible systems, methods preserving first integrals and numerical methods on manifolds, including Lie group methods and integrators for constrained mechanical systems, and methods for problems with highly oscillatory solutions. A complete theory of symplectic and symmetric 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 and related perturbation theories. The book is illustrated by many figures, it treats applications from physics and astronomy and contains many numerical experiments and comparisons of different approaches |
| Beschreibung: | 1 Online-Ressource (XIII, 515 p) |
| ISBN: | 9783662050187 9783662050200 |
| ISSN: | 0179-3632 |
| DOI: | 10.1007/978-3-662-05018-7 |
Internformat
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Datensatz im Suchindex
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-05018-7 |
| format | Electronic eBook |
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| institution | BVB |
| isbn | 9783662050187 9783662050200 |
| issn | 0179-3632 |
| language | English |
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| spelling | Hairer, Ernst Verfasser aut Geometric Numerical Integration Structure-Preserving Algorithms for Ordinary Differential Equations by Ernst Hairer, Gerhard Wanner, Christian Lubich Berlin, Heidelberg Springer Berlin Heidelberg 2002 1 Online-Ressource (XIII, 515 p) txt rdacontent c rdamedia cr rdacarrier Springer Series in Computational Mathematics 31 0179-3632 The subject of this book is numerical methods that preserve geometric properties of the flow of a differential equation: symplectic integrators for Hamiltonian systems, symmetric integrators for reversible systems, methods preserving first integrals and numerical methods on manifolds, including Lie group methods and integrators for constrained mechanical systems, and methods for problems with highly oscillatory solutions. A complete theory of symplectic and symmetric 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 and related perturbation theories. The book is illustrated by many figures, it treats applications from physics and astronomy and contains many numerical experiments and comparisons of different approaches Mathematics Global analysis (Mathematics) Numerical analysis Mathematical physics Numerical Analysis Analysis Theoretical, Mathematical and Computational Physics Mathematical Methods in Physics Numerical and Computational Physics Mathematical and Computational Biology Mathematik Mathematische Physik Numerische Integration (DE-588)4172168-8 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Numerische Integration (DE-588)4172168-8 s 1\p DE-604 Wanner, Gerhard Sonstige oth Lubich, Christian Sonstige oth https://doi.org/10.1007/978-3-662-05018-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hairer, Ernst Geometric Numerical Integration Structure-Preserving Algorithms for Ordinary Differential Equations Mathematics Global analysis (Mathematics) Numerical analysis Mathematical physics Numerical Analysis Analysis Theoretical, Mathematical and Computational Physics Mathematical Methods in Physics Numerical and Computational Physics Mathematical and Computational Biology Mathematik Mathematische Physik Numerische Integration (DE-588)4172168-8 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4172168-8 (DE-588)4020929-5 |
| title | Geometric Numerical Integration Structure-Preserving Algorithms for Ordinary Differential Equations |
| title_auth | Geometric Numerical Integration Structure-Preserving Algorithms for Ordinary Differential Equations |
| title_exact_search | Geometric Numerical Integration Structure-Preserving Algorithms for Ordinary Differential Equations |
| title_full | Geometric Numerical Integration Structure-Preserving Algorithms for Ordinary Differential Equations by Ernst Hairer, Gerhard Wanner, Christian Lubich |
| title_fullStr | Geometric Numerical Integration Structure-Preserving Algorithms for Ordinary Differential Equations by Ernst Hairer, Gerhard Wanner, Christian Lubich |
| title_full_unstemmed | Geometric Numerical Integration Structure-Preserving Algorithms for Ordinary Differential Equations by Ernst Hairer, Gerhard Wanner, Christian Lubich |
| title_short | Geometric Numerical Integration |
| title_sort | geometric numerical integration structure preserving algorithms for ordinary differential equations |
| title_sub | Structure-Preserving Algorithms for Ordinary Differential Equations |
| topic | Mathematics Global analysis (Mathematics) Numerical analysis Mathematical physics Numerical Analysis Analysis Theoretical, Mathematical and Computational Physics Mathematical Methods in Physics Numerical and Computational Physics Mathematical and Computational Biology Mathematik Mathematische Physik Numerische Integration (DE-588)4172168-8 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Numerical analysis Mathematical physics Numerical Analysis Analysis Theoretical, Mathematical and Computational Physics Mathematical Methods in Physics Numerical and Computational Physics Mathematical and Computational Biology Mathematik Mathematische Physik Numerische Integration Gewöhnliche Differentialgleichung |
| url | https://doi.org/10.1007/978-3-662-05018-7 |
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