عنوان
پدید آورنده
موضوع
رده
کتابخانه
محل استقرار
INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
9783662050187
(Number (ISBN
9783662050200
NATIONAL BIBLIOGRAPHY NUMBER
Number
b407843
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
Geometric Numerical Integration
General Material Designation
[Book]
Other Title Information
Structure-Preserving Algorithms for Ordinary Differential Equations /
First Statement of Responsibility
by Ernst Hairer, Gerhard Wanner, Christian Lubich.
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Berlin, Heidelberg :
Name of Publisher, Distributor, etc.
Imprint: Springer,
Date of Publication, Distribution, etc.
2002.
SERIES
Series Title
Springer Series in Computational Mathematics,
Volume Designation
31
ISSN of Series
0179-3632 ;
CONTENTS NOTE
Text of Note
I. Examples and Numerical Experiments -- II. Numerical Integrators -- 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.
0
SUMMARY OR ABSTRACT
Text of Note
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.
OTHER EDITION IN ANOTHER MEDIUM
International Standard Book Number
9783662050200
PIECE
Title
Springer eBooks
TOPICAL NAME USED AS SUBJECT
Global analysis (Mathematics).
Mathematical physics.
Mathematics.
Numerical analysis.
PERSONAL NAME - PRIMARY RESPONSIBILITY
Hairer, Ernst.
PERSONAL NAME - ALTERNATIVE RESPONSIBILITY
Lubich, Christian.
Wanner, Gerhard.
CORPORATE BODY NAME - ALTERNATIVE RESPONSIBILITY
SpringerLink (Online service)
ORIGINATING SOURCE
Date of Transaction
20190301082600.0
ELECTRONIC LOCATION AND ACCESS
Electronic name
مطالعه متن کتاب [Book]
Y
