Item description for Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations (Springer Series in Computational Mathematics) by Ernst Hairer, Christian Lubich & Gerhard Wanner...
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.
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Est. Packaging Dimensions: Length: 1.25" Width: 6.25" Height: 9.25" Weight: 2.32 lbs.
Release Date Apr 28, 2006
ISBN 3540306633 ISBN13 9783540306634
Availability 0 units.
More About Ernst Hairer, Christian Lubich & Gerhard Wanner
Ernst Hairer is a Professor of Mathematics at the University of Geneva and has been awarded the Henrici Prize by the Society of Industrial and Applied Mathematics.
Ernst Hairer has an academic affiliation as follows - Universit?? de Gen??ve Universite de Geneve Universite de Geneve Unive.
Reviews - What do customers think about Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations (Springer Series in Computational Mathematics)?
The Numerical Bible May 27, 2008
Why be interested in geometric numerical integrators you ask? Well, if you want algorithms that are accurate and conserve geometric properties of the dynamical flow you have to look at geometric integrators. For instance, in Hamiltonian systems the flow preserves the symplectic two-form (the volume of the phase space), and symplectic integrators do exactly that, which means that these algorithms are more accurate than their non-symplectic counterparts: conserved quantities are really conserved numerically.
Geometric Numerical Integration deals with the foundations, examples and actual applications of geometric integrators in various fields of research, and there is a lot on the more abstract theory of numerical mathematics, the classification of algorithms, provided with lots of mathematical and physical background needed to understand what is special about certain algorithms and advice on when, where and how to use them. It is completely self-contained, up-to-date, clear, well written, it has many references, and it is aimed at students and scientist who want to learn more about everything there is to know on geometric integrators.
Admittedly, it is not completely inexpensive, but considering it is probably the only book you'll ever have to buy on geometric numerical integration and the fact that it looks great and is made very well, it is well worth the money!