Springer Series in Computational Mathematics

Geometric Numerical Integration

Structure-Preserving Algorithms for Ordinary Differential Equations

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

Buy this book

eBook $89.00
price for USA (gross)
  • ISBN 978-3-540-30666-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $199.00
price for USA
  • ISBN 978-3-540-30663-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $119.00
price for USA
  • ISBN 978-3-642-05157-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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)


Table of contents (5 chapters)

  • Examples and Numerical Experiments

    Ernst Hairer, Gerhard Wanner, Christian Lubich

    Pages 1-26

  • Numerical Integrators

    Ernst Hairer, Gerhard Wanner, Christian Lubich

    Pages 27-50

  • Order Conditions, Trees and B-Series

    Ernst Hairer, Gerhard Wanner, Christian Lubich

    Pages 51-96

  • Conservation of First Integrals and Methods on Manifolds

    Ernst Hairer, Gerhard Wanner, Christian Lubich

    Pages 97-142

  • Symmetric Integration and Reversibility

    Ernst Hairer, Gerhard Wanner, Christian Lubich

    Pages 143-178

Buy this book

eBook $89.00
price for USA (gross)
  • ISBN 978-3-540-30666-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $199.00
price for USA
  • ISBN 978-3-540-30663-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $119.00
price for USA
  • ISBN 978-3-642-05157-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Loading...

Recommended for you

Loading...

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
2006
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-30666-5
DOI
10.1007/3-540-30666-8
Hardcover ISBN
978-3-540-30663-4
Softcover ISBN
978-3-642-05157-9
Series ISSN
0179-3632
Edition Number
2
Number of Pages
XVI, 644
Topics