Geometric numerical integration structure-preserving algorithms for ordinary differential equations Ernst Hairer, Christian Lubich, Gerhard Wanner. Springer series in computational mathematics 31.

Hairer, Ernst:

ISBN 10: 3540430032 / ISBN 13: 9783540430032

Editore: Berlin, Springer [2002]., 2002

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Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ancien Exemplaire de bibliothèque avec signature et cachet. BON état, quelques traces d'usure. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. 65 HAI 9783540430032 Sprache: Englisch Gewicht in Gramm: 1150.

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Dati bibliografici

• Titolo: Geometric numerical integration structure-preserving algorithms for ordinary differential equations Ernst Hairer, Christian Lubich, Gerhard Wanner. Springer series in computational mathematics 31.
• Editore: Berlin, Springer [2002].
• Data di pubblicazione: 2002
• Lingua: Inglese
• ISBN 10: 3540430032
• ISBN 13: 9783540430032
• Rilegatura: Hardcover
• Peso: 1150 grammi
• Cataloghi dei venditori:
  • SA MATHEMATIK

Descrizione articolo

Riassunto

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.

Dalla quarta di copertina

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.