Geometric Numerical Integration of Differential Equations: Titles and Abstracts
Neuware - 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.
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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. Brand new book, sourced directly from publisher.
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Ebook Structure Preserving Algorithms For Oscillatory Differential Equations 2013
Publisher: Springer , This specific ISBN edition is currently not available. View all copies of this ISBN edition:. Synopsis About this title This book covers numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. Buy New Learn more about this copy. Other Popular Editions of the Same Title. Springer, Hardcover.
Search for all books with this author and title. Such systems arise in many branches of science and engineering, and the examples in the book include systems from quantum physics, celestial mechanics and electronics.
To accurately simulate the true behavior of such systems, a numerical algorithm must preserve as much as possible their key structural properties: time-reversibility, oscillation, symplecticity, and energy and momentum conservation. The accuracy and efficiency of each of these algorithms are tested via careful numerical simulations, and their structure-preserving properties are rigorously established by theoretical analysis. The book also gives insights into the practical implementation of the methods.
This book is intended for engineers and scientists investigating oscillatory systems, as well as for teachers and students who are interested in structure-preserving algorithms for differential equations. Senior undergraduate and graduate students of applied mathematics, engineering and physics will find the book to be an invaluable resource. It can also be used as a textbook in courses on structure preserving numerical algorithms for IVPs.
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This collection of scientific work is suitable for researchers as well as postgraduate students Ph. Lubich, G. Springer, Berlin, , 2nd edition Leimkuhler, S. Press, Oberwolfach Rep.