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Geometric Numerical Integration

Structure-Preserving Algorithms for Ordinary Differential Equations

Ernst Hairer, Christian Lubich, Gerhard Wanner (Autoren)

Buch | Hardcover

XVI, 644 Seiten

2006 | 2nd ed. 2006
Springer Berlin (Verlag)
978-3-540-30663-4 (ISBN)

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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.

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.

Erscheint lt. Verlag	22.2.2006
Reihe/Serie	Springer Series in Computational Mathematics
Zusatzinfo	XVI, 644 p.
Verlagsort	Berlin
Sprache	englisch
Maße	210 x 297 mm
Gewicht	2430 g
Themenwelt	Informatik ► Weitere Themen ► Bioinformatik
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
	Naturwissenschaften ► Physik / Astronomie
Schlagworte	algorithms • Calculus • Differential equations on manifolds • Geometric numerical integration • Hamiltonian and reversible systems • Numerical Integration • Symplectic and symmetric methods
ISBN-10	3-540-30663-3 / 3540306633
ISBN-13	978-3-540-30663-4 / 9783540306634
Zustand	Neuware