Simulating Hamiltonian dynamics:
Geometric integrators are time-stepping methods, designed such that they exactly satisfy conservation laws, symmetries or symplectic properties of a system of differential equations. In this book the authors outline the principles of geometric integration and demonstrate how they can be applied to p...
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| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2004
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| Schriftenreihe: | Cambridge monographs on applied and computational mathematics
14 |
| Links: | https://doi.org/10.1017/CBO9780511614118 |
| Zusammenfassung: | Geometric integrators are time-stepping methods, designed such that they exactly satisfy conservation laws, symmetries or symplectic properties of a system of differential equations. In this book the authors outline the principles of geometric integration and demonstrate how they can be applied to provide efficient numerical methods for simulating conservative models. Beginning from basic principles and continuing with discussions regarding the advantageous properties of such schemes, the book introduces methods for the N-body problem, systems with holonomic constraints, and rigid bodies. More advanced topics treated include high-order and variable stepsize methods, schemes for treating problems involving multiple time-scales, and applications to molecular dynamics and partial differential equations. The emphasis is on providing a unified theoretical framework as well as a practical guide for users. The inclusion of examples, background material and exercises enhance the usefulness of the book for self-instruction or as a text for a graduate course on the subject. |
| Umfang: | 1 Online-Ressource (xvi, 379 Seiten) |
| ISBN: | 9780511614118 |
Internformat
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| spelling | Leimkuhler, B. Simulating Hamiltonian dynamics Benedict Leimkuhler, Sebastian Reich Cambridge Cambridge University Press 2004 1 Online-Ressource (xvi, 379 Seiten) txt c cr Cambridge monographs on applied and computational mathematics 14 Geometric integrators are time-stepping methods, designed such that they exactly satisfy conservation laws, symmetries or symplectic properties of a system of differential equations. In this book the authors outline the principles of geometric integration and demonstrate how they can be applied to provide efficient numerical methods for simulating conservative models. Beginning from basic principles and continuing with discussions regarding the advantageous properties of such schemes, the book introduces methods for the N-body problem, systems with holonomic constraints, and rigid bodies. More advanced topics treated include high-order and variable stepsize methods, schemes for treating problems involving multiple time-scales, and applications to molecular dynamics and partial differential equations. The emphasis is on providing a unified theoretical framework as well as a practical guide for users. The inclusion of examples, background material and exercises enhance the usefulness of the book for self-instruction or as a text for a graduate course on the subject. Reich, Sebastian Erscheint auch als Druck-Ausgabe 9780521772907 |
| spellingShingle | Leimkuhler, B. Simulating Hamiltonian dynamics |
| title | Simulating Hamiltonian dynamics |
| title_auth | Simulating Hamiltonian dynamics |
| title_exact_search | Simulating Hamiltonian dynamics |
| title_full | Simulating Hamiltonian dynamics Benedict Leimkuhler, Sebastian Reich |
| title_fullStr | Simulating Hamiltonian dynamics Benedict Leimkuhler, Sebastian Reich |
| title_full_unstemmed | Simulating Hamiltonian dynamics Benedict Leimkuhler, Sebastian Reich |
| title_short | Simulating Hamiltonian dynamics |
| title_sort | simulating hamiltonian dynamics |
| work_keys_str_mv | AT leimkuhlerb simulatinghamiltoniandynamics AT reichsebastian simulatinghamiltoniandynamics |