Geometric numerical integration
structure-preserving algorithms for ordinary differential equations
Hairer, E. (Ernst)
creator
Lubich, Christian
1959-
author
Wanner, Gerhard
author
text
bibliography
gw
2010
Second edition
monographic
eng
xvii, 644 pages : illustrations ; 25 cm.
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.
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.
Ernst Hairer, Christian Lubich, Gerhard Wanner.
Include index
Includes bibliographical references (p. [617]-636) and index.
Differential equations
Numerical solutions
Hamiltonian systems
Numerical integration
Mathematical physics
Numerical analysis
515.352 H1537g 2010
9783642051579 (softcover)
2010922987
http://www.loc.gov/catdir/enhancements/fy1317/2010922987-d.html
http://www.loc.gov/catdir/enhancements/fy1402/2010922987-t.html
http://www.loc.gov/catdir/enhancements/fy1317/2010922987-d.html
http://www.loc.gov/catdir/enhancements/fy1402/2010922987-t.html
DLC
100218
20200513144338.0
16095817