| Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations 2006 Edition Contributor(s): Hairer, Ernst (Author), Lubich, Christian (Author), Wanner, Gerhard (Author) |
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ISBN: 3540306633 ISBN-13: 9783540306634 Publisher: Springer OUR PRICE: $237.49 Product Type: Hardcover - Other Formats Published: February 2006 Annotation: 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. |
| Additional Information |
| BISAC Categories: - Science | Physics - Mathematical & Computational - Mathematics | Number Systems - Mathematics | Mathematical Analysis |
| Dewey: 515.352 |
| LCCN: 2005938386 |
| Series: Springer Series in Computational Mathematics |
| Physical Information: 1.13" H x 6.58" W x 9.41" (2.29 lbs) 644 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |