Geometric Numerical Integration

Structure-Preserving Algorithms for Ordinary Differential Equations
2. Auflage 2006. 2. printing 2010
ISBN: 978-3-642-05157-9
Verlag: Springer

Buch, Englisch, Band 31, 644 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 2020 g

Reihe: Springer Series in Computational Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Hairer, Ernst

Lubich, Christian

Wanner, Gerhard

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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.