Ernst Hairer, Christian Lubich, Gerhard Wanner

Geometric Numerical Integration (eBook, PDF)

Structure-Preserving Algorithms for Ordinary Differential Equations

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 644
• Erscheinungstermin: 18. Mai 2006
• Englisch
• ISBN-13: 9783540306665
• Artikelnr.: 37366415

Autorenporträt

Ernst Hairer, University of Geneva, Switzerland / Christian Lubich, University of Tübingen, Germany / Gerhard Wanner, University of Geneva, Switzerland

Inhaltsangabe

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.