E-Book, Englisch, 515 Seiten, Web PDF
Hairer / Lubich / Wanner Geometric Numerical Integration
Erscheinungsjahr 2013
ISBN: 978-3-662-05018-7
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
Structure-Preserving Algorithms for Ordinary Differential Equations
E-Book, Englisch, 515 Seiten, Web PDF
Reihe: Springer Series in Computational Mathematics
ISBN: 978-3-662-05018-7
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Zielgruppe
Research
Autoren/Hrsg.
Weitere Infos & Material
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.
