Articoli correlati a Geometric Numerical Integration: Structure-Preserving...
Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations: 31 - Rilegato
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This book covers numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. It presents a
theory of symplectic and symmetric methods, which include various specially designed integrators, as well as discusses their construction and practical merits. The long-time behavior of the numerical solutions is studied using a backward error analysis combined with KAM theory.
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
Recensione
From the reviews of the second edition:
"This book is highly recommended for advanced courses in numerical methods for ordinary differential equations as well as a reference for researchers/developers in the field of geometric integration, differential equations in general and related subjects. It is a must for academic and industrial libraries." -- MATHEMATICAL REVIEWS
"The second revised edition of the monograph is a fine work organized in fifteen chapters, updated and extended. ... The material of the book is organized in sections which are ... self-contained, so that one can dip into the book to learn a particular topic ... . A person interested in geometrical numerical integration will find this book extremely useful." (Calin Ioan Gheorghiu, Zentralblatt MATH, Vol. 1094 (20), 2006)
Contenuti
Examples and Numerical Experiments.- Numerical Integrators.- Order Conditions, Trees and B-Series.- Conservation of First Integrals and Methods on Manifolds.- Symmetric Integration and Reversibility.- Symplectic Integration of Hamiltonian Systems.- Non-Canonical Hamiltonian Systems.- Structure-Preserving Implementation.- Backward Error Analysis and Structure Preservation.- Hamiltonian Perturbation Theory and Symplectic Integrators.- Reversible Perturbation Theory and Symmetric Integrators.- Dissipatively Perturbed Hamiltonian and Reversible Systems.- Oscillatory Differential Equations with Constant High Frequencies.- Oscillatory Differential Equations with Varying High Frequencies.- Dynamics of Multistep Methods.
Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.
- EditoreSpringer Nature
- Data di pubblicazione2006
- ISBN 10 3540306633
- ISBN 13 9783540306634
- RilegaturaCopertina rigida
- LinguaInglese
- Numero edizione2
- Numero di pagine644
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Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations (Springer Series in Computational Mathematics, 31)
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Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations (Springer Series in Computational Mathematics, 31)
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Geometric Numerical Integration
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This book covers numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. It presents atheory of symplectic and symmetric methods, wh. Codice articolo 458667327
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Geometric Numerical Integration
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ISBN 10: 3540306633
ISBN 13: 9783540306634
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 664 pp. Englisch. Codice articolo 9783540306634
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Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations (Springer Series in Computational Mathematics, 31)
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Geometric Numerical Integration : Structure-Preserving Algorithms for Ordinary Differential Equations
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Springer Berlin Heidelberg, Springer Berlin Heidelberg, 2006
ISBN 10: 3540306633
ISBN 13: 9783540306634
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Buch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Codice articolo 9783540306634
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Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations (Springer Series in Computational Mathematics, 31)
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Hardcover. Condizione: Brand New. 2nd edition. 644 pages. 9.25x6.25x1.25 inches. In Stock. Codice articolo x-3540306633
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