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© 2006

Geometric Numerical Integration

Structure-Preserving Algorithms for Ordinary Differential Equations

Book

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 31)

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 1-26
  3. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 27-50
  4. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 51-96
  5. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 97-142
  6. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 143-178
  7. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 179-236
  8. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 237-302
  9. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 303-336
  10. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 337-388
  11. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 389-436
  12. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 437-454
  13. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 455-470
  14. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 471-530
  15. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 531-565
  16. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 567-616
  17. Back Matter
    Pages 617-644

About this book

Introduction

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.

Keywords

Hamiltonian and reversible systems Numerical integration algorithms calculus differential equations on manifolds geometric numerical integration symplectic and symmetric methods

Authors and affiliations

  1. 1.Section de MathématiquesUniversité de GenèveGenève 4Switzerland
  2. 2.Section de MathématiquesUniversité de GenèveGenève 4Switzerland
  3. 3.Mathematisches InstitutUniversität TübingenTübingenGermany

Bibliographic information

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)