Author	Hairer, Ernst. author
Title	Geometric Numerical Integration [electronic resource] : Structure-Preserving Algorithms for Ordinary Differential Equations / by Ernst Hairer, Gerhard Wanner, Christian Lubich
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002
Connect to	http://dx.doi.org/10.1007/978-3-662-05018-7
Descript	XIII, 515 p. 224 illus. online resource

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

I. Examples and Numerical Experiments -- II. Numerical Integrators -- III. Order Conditions, Trees and B-Series -- IV. Conservation of First Integrals and Methods on Manifolds -- V. Symmetric Integration and Reversibility -- VI. Symplectic Integration of Hamiltonian Systems -- VII. Further Topics in Structure Preservation -- VIII. Structure-Preserving Implementation -- IX. Backward Error Analysis and Structure Preservation -- X. Hamiltonian Perturbation Theory and Symplectic Integrators -- XI Reversible Perturbation Theory and Symmetric Integrators -- XII. Dissipatively Perturbed Hamiltonian and Reversible Systems -- XIII. Highly Oscillatory Differential Equations -- XIV. Dynamics of Multistep Methods

1. Mathematics
2. Mathematical analysis
3. Analysis (Mathematics)
4. Numerical analysis
5. Biomathematics
6. Physics
7. Mathematics
8. Numerical Analysis
9. Analysis
10. Theoretical
11. Mathematical and Computational Physics
12. Mathematical Methods in Physics
13. Numerical and Computational Physics
14. Mathematical and Computational Biology