Simulating Hamiltonian Dynamics
Simulating Hamiltonian Dynamics
Sebastian Reich, Imperial College of Science, Technology and Medicine, London
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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.
- Thorough treatment of a relatively new subject, covers theory, applications and also gives practical advice on implementing the techniques
- Emphasis on 'efficient' numerical methods
- Large number of examples and exercises
Reviews & endorsements
"Overall this is a book to be strongly recommended both for individual study and as the basis for a graduate course to a wide range of students. The arrangement of the chapters means that the description of the numerical methods and their properties is never far away from the applications that have motivated their development...Each chapter contains a set of exercises which are often quite short but very illuminating."
SIAM Review
Product details
February 2005Hardback
9780521772907
396 pages
235 × 160 × 23 mm
0.75kg
71 b/w illus. 5 tables 80 exercises
Available
Table of Contents
- 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.
