Geometric Numerical Integration Structure-Preserving Algorithms for Ordinary Differential Equations /

• Main Authors: Hairer, Ernst (Author), Wanner, Gerhard (Author), Lubich, Christian (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Series: Springer Series in Computational Mathematics, 31
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Numerical analysis.; Biomathematics.; Physics.; Numerical Analysis.; Analysis.; Theoretical, Mathematical and Computational Physics.; Mathematical Methods in Physics.; Numerical and Computational Physics.; Mathematical and Computational Biology.

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, com...

Table of Contents:

• 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.