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Geometric Numerical Integration

Structure-Preserving Algorithms for Ordinary Differential Equations

  • Book
  • © 2002

Overview

Authors:
  1. Ernst Hairer

    1. Section de Mathématiques, Université de Genève, Genève 24, Switzerland

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  2. Gerhard Wanner

    1. Section de Mathématiques, Université de Genève, Genève 24, Switzerland

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    You can also search for this author in PubMed   Google Scholar

  3. Christian Lubich

    1. Mathematisches Institut, Universtität Tübingen, Tübingen, Germany

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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
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Examples and Numerical Experiments

    • Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 1-22

  3. Numerical Integrators

    • Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 23-46

  4. Order Conditions, Trees and B-Series

    • Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 47-92

  5. Conservation of First Integrals and Methods on Manifolds

    • Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 93-130

  6. Symmetric Integration and Reversibility

    • Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 131-166

  7. Symplectic Integration of Hamiltonian Systems

    • Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 167-208

  8. Further Topics in Structure Preservation

    • Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 209-254

  9. Structure-Preserving Implementation

    • Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 255-286

  10. Backward Error Analysis and Structure Preservation

    • Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 287-326

  11. Hamiltonian Perturbation Theory and Symplectic Integrators

    • Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 327-374

  12. Reversible Perturbation Theory and Symmetric Integrators

    • Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 375-390

  13. Dissipatively Perturbed Hamiltonian and Reversible Systems

    • Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 391-406

  14. Highly Oscillatory Differential Equations

    • Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 407-453

  15. Dynamics of Multistep Methods

    • Ernst Hairer, Gerhard Wanner, Christian Lubich
    Pages 455-491

  16. Back Matter

    Pages 493-515
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Keywords

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.

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

Authors and Affiliations

  • Section de Mathématiques, Université de Genève, Genève 24, Switzerland

    Ernst Hairer, Gerhard Wanner

  • Mathematisches Institut, Universtität Tübingen, Tübingen, Germany

    Christian Lubich

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