An edition of Geometric Numerical Integration (2002)

Geometric Numerical Integration

Structure-Preserving Algorithms for Ordinary Differential Equations

by

Cover of: Geometric Numerical Integration by Ernst Hairer, Ernst Hairer
Locate

My Reading Lists:

Create a new list

Check-In

×Close
Add an optional check-in date. Check-in dates are used to track yearly reading goals.
Today
Notes
Notes

Check nearby libraries

Buy this book

Last edited by ImportBot
February 27, 2022 | History
Edit
An edition of Geometric Numerical Integration (2002)

Geometric Numerical Integration

Structure-Preserving Algorithms for Ordinary Differential Equations

by

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.

Publish Date
Publisher
Springer Berlin Heidelberg
Language
English
Pages
515

Check nearby libraries

Buy this book

Previews available in: English

Subjects

Mathematics, Numerical analysis, Global analysis (Mathematics), Mathematical physics, Number systems, Mathematical analysis, Mathematical & computational, Applied, Mathematics & statistics -> mathematics -> mathematics general, Physical & earth sciences -> physics -> mathematical physics, Scm14050, Scm12007, Scp19005, Scp19013, Scp19021, Scm31000, Suco11649, 3640, 3076, 2998, 5270, 3021
Edition Availability
Cover of: Geometric Numerical Integration
Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations
Sep 02, 2009, Springer
paperback
Cover of: Geometric Numerical Integration
Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations
2006, Springer London, Limited
in English
Cover of: Geometric Numerical Integration
Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations
2002, Springer Berlin Heidelberg
electronic resource : in English

Add another edition?

Book Details

Table of Contents

I. Examples and Numerical Experiments
II. Numerical Integrator
III. Order-Conditions, Trees, and B-Series
IV. Conservation of First Integrals and Methods on Manifolds
V. Symmetric Integration and Reversibility
VI. Symplectic Integration of Hamiltonian Systems
VII. Further Topics in Structure Preservation. - VIII. Structure-Preserving Implementation
IX. Backward Error Analysis and Structure Preservation
X. Hamiltonian Perturbation Theory and Symplectic Integrators
XI. Reversible Perturbation Theory and Symmetric Integrators
XII. Dissipatively Perturbed Hamiltonian and Reversible Systems
XIII. Highly Oscillatory Differential Equations
XIV. Dynamics of Multistep Methods
Bibliography.

Edition Notes

Online full text is restricted to subscribers.

Also available in print.

Mode of access: World Wide Web.

Published in
Berlin, Heidelberg
Series
Springer Series in Computational Mathematics -- 31, Springer Series in Computational Mathematics -- 31

Classifications

Dewey Decimal Class
518
Library of Congress
QA297-299.4

The Physical Object

Format
[electronic resource] :
Pagination
1 online resource (xiii, 515 p.)
Number of pages
515

ID Numbers

Open Library
OL27041007M
Internet Archive
geometricnumeric00hair_654
ISBN 10
366205020X, 3662050188
ISBN 13
9783662050200, 9783662050187
OCLC/WorldCat
851368851

Source records

Internet Archive item record
Internet Archive item record
Better World Books record

Community Reviews (0)

Feedback?
No community reviews have been submitted for this work.

Lists

This work does not appear on any lists.

History

Download catalog record: RDF / JSON / OPDS | Wikipedia citation
February 27, 2022 Edited by ImportBot import existing book
June 30, 2019 Edited by MARC Bot import existing book
June 30, 2019 Created by MARC Bot Imported from Internet Archive item record