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Springer Series in Computational Mathematics

Geometric Numerical Integration

Structure-Preserving Algorithms for Ordinary Differential Equations

Authors: Hairer, Ernst, Lubich, Christian, Wanner, Gerhard

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  • A unique feature of the book is the numerical treatment of KAM theory
  • There is no other book which deals with this
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  • ISBN 978-3-662-05018-7
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About this book

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.

Reviews

"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

Table of contents (14 chapters)

Table of contents (14 chapters)

Buy this book

eBook 67,40 €
price for Spain (gross)
  • ISBN 978-3-662-05018-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Geometric Numerical Integration
Book Subtitle
Structure-Preserving Algorithms for Ordinary Differential Equations
Authors
Series Title
Springer Series in Computational Mathematics
Series Volume
31
Copyright
2002
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-05018-7
DOI
10.1007/978-3-662-05018-7
Series ISSN
0179-3632
Edition Number
1
Number of Pages
XIII, 515
Number of Illustrations
224 b/w illustrations
Topics

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