Geometric Numerical Integration

Structure-Preserving Algorithms for Ordinary Differential Equations

  • Ernst Hairer
  • Gerhard Wanner
  • Christian Lubich

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

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 1-22
  3. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 23-46
  4. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 47-92
  5. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 93-130
  6. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 131-166
  7. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 167-208
  8. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 209-254
  9. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 255-286
  10. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 287-326
  11. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 327-374
  12. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 375-390
  13. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 391-406
  14. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 407-453
  15. Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 455-491
  16. Back Matter
    Pages 493-515

About this book

Introduction

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.

Keywords

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

Authors and affiliations

  • Ernst Hairer
    • 1
  • Gerhard Wanner
    • 1
  • Christian Lubich
    • 2
  1. 1.Section de MathématiquesUniversité de GenèveGenève 24Switzerland
  2. 2.Mathematisches InstitutUniverstität TübingenTübingenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-05018-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2002
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-05020-0
  • Online ISBN 978-3-662-05018-7
  • Series Print ISSN 0179-3632
  • About this book
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