Simulating Hamiltonian Dynamics
Seiten
2005
Cambridge University Press (Verlag)
978-0-521-77290-7 (ISBN)
Cambridge University Press (Verlag)
978-0-521-77290-7 (ISBN)
Geometric integrators are time-stepping methods, designed to exactly satisfy properties inherent in a system of differential equations. Beginning from basic principles of geometric integration and a discussion of the advantageous properties of such schemes, the book introduces a variety of methods and applications. Includes examples and exercises.
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.
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.
Ben Leimkuhler is Professor of Applied Mathematics, and Director of the Centre for Mathematical Modelling at the University of Leicester. Sebastian Reich is Professor of Computational and Mathematical Modelling at Imperial College London.
1. Introduction; 2. Numerical methods; 3. Hamiltonian mechanics; 4. Geometric integrators; 5. The modified equations; 6. Higher order methods; 7. Contained mechanical systems; 8. Rigid Body dynamics; 9. Adaptive geometric integrators; 10. Highly oscillatory problems; 11. Molecular dynamics; 12. Hamiltonian PDEs.
| Erscheint lt. Verlag | 14.2.2005 |
|---|---|
| Reihe/Serie | Cambridge Monographs on Applied and Computational Mathematics |
| Zusatzinfo | Worked examples or Exercises; 5 Tables, unspecified; 71 Line drawings, unspecified |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 160 x 235 mm |
| Gewicht | 750 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 0-521-77290-7 / 0521772907 |
| ISBN-13 | 978-0-521-77290-7 / 9780521772907 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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