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Geometric Numerical Integration: Structure-preserving Algorithms for Ordinary Differential Equations: v.31 (Springer Series in Computational Mathematics) - Hardcover
Synopsis
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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Review
"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
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Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations
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Geometric numerical integration structure-preserving algorithms for ordinary differential equations Ernst Hairer, Christian Lubich, Gerhard Wanner. Springer series in computational mathematics 31.
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Berlin, Springer [2002]., 2002
ISBN 10: 3540430032
ISBN 13: 9783540430032
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Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations
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