| 書目名稱 | Geometric Numerical Integration | | 副標題 | Structure-Preserving | | 編輯 | Ernst Hairer,Gerhard Wanner,Christian Lubich | | 視頻video | http://file.papertrans.cn/384/383580/383580.mp4 | | 叢書名稱 | Springer Series in Computational Mathematics | | 圖書封面 |  | | 描述 | .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.. | | 出版日期 | Book 2006Latest edition | | 關鍵詞 | Hamiltonian and reversible systems; Numerical integration; algorithms; calculus; differential equations | | 版次 | 2 | | doi | https://doi.org/10.1007/3-540-30666-8 | | isbn_softcover | 978-3-642-05157-9 | | isbn_ebook | 978-3-540-30666-5Series ISSN 0179-3632 Series E-ISSN 2198-3712 | | issn_series | 0179-3632 | | copyright | Springer-Verlag Berlin Heidelberg 2006 |
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