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Table of contents (15 chapters)
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Front Matter
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Back Matter
About this book
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.
Reviews
From the reviews of the second edition:
"This book is highly recommended for advanced courses in numerical methods for ordinary differential equations as well as a reference for researchers/developers in the field of geometric integration, differential equations in general and related subjects. It is a must for academic and industrial libraries." -- MATHEMATICAL REVIEWS
"The second revised edition of the monograph is a fine work organized in fifteen chapters, updated and extended. … The material of the book is organized in sections which are … self-contained, so that one can dip into the book to learn a particular topic … . A person interested in geometrical numerical integration will find this book extremely useful." (Calin Ioan Gheorghiu, Zentralblatt MATH, Vol. 1094 (20), 2006)
Authors and Affiliations
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Section de Mathématiques, Université de Genève, Genève 4, Switzerland
Ernst Hairer, Gerhard Wanner
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Mathematisches Institut, Universität Tübingen, Tübingen, Germany
Christian Lubich
Bibliographic Information
Book Title: Geometric Numerical Integration
Book Subtitle: Structure-Preserving Algorithms for Ordinary Differential Equations
Authors: Ernst Hairer, Gerhard Wanner, Christian Lubich
Series Title: Springer Series in Computational Mathematics
DOI: https://doi.org/10.1007/3-540-30666-8
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2006
Hardcover ISBN: 978-3-540-30663-4Published: 22 February 2006
Softcover ISBN: 978-3-642-05157-9Published: 11 March 2010
eBook ISBN: 978-3-540-30666-5Published: 18 May 2006
Series ISSN: 0179-3632
Series E-ISSN: 2198-3712
Edition Number: 2
Number of Pages: XVI, 644
Topics: Numerical Analysis, Analysis, Theoretical, Mathematical and Computational Physics, Mathematical Methods in Physics, Numerical and Computational Physics, Simulation, Mathematical and Computational Biology