Hairer, E.

Geometric numerical integration : structure-preserving algorithms for ordinary differential equations / Ernst Hairer, Christian Lubich, Gerhard Wanner. - Second edition - xvii, 644 pages : illustrations ; 25 cm. - Springer series in computational mathematics 31 0179-3632 ; .

Include index

Includes bibliographical references (p. [617]-636) and index.

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 -- Dissipative perturbed Hamiltonian and reversible systems -- Oscillatory diffential equations with constant high frequencies -- Oscillatory differential equations with varying high frequencies -- Dynamics of multistep methods.

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, 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. The book is illustrated by many figures, it treats applications from physics and astronomy and contains many numerical experiments and comparisons of different approaches. The second edition is substantially revised and enlarged, with many improvements in the presentation and additions concerning in particular non-canonical Hamiltonian systems, highly oscillatory mechanical systems, and the dynamics of multistep methods.

9783642051579 (softcover)


Differential equations--Numerical solutions
Hamiltonian systems.
Numerical integration
Mathematical physics
Numerical analysis

515.352 / H1537g 2010