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Simulating Hamiltonian Dynamics Benedict Leimkuhler (University of Leicester)

Simulating Hamiltonian Dynamics By Benedict Leimkuhler (University of Leicester)

Summary

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.

Simulating Hamiltonian Dynamics Summary

Simulating Hamiltonian Dynamics by Benedict Leimkuhler (University of Leicester)

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.

Simulating Hamiltonian Dynamics Reviews

' this new book on geometric integration of Hamiltonian systems is a valuable addition to the subject that may be very useful not only as a textbook for courses in computational dynamics but also for researchers in the design of effective integrators in molecular dynamics and other areas of applied mathematics because it includes most of the recent research in the subject.' Zentralblatt MATH
'I highly recommend it for a graduate course on multivariate approximation theory, computer-aided geometric design, and meshless methods for partial differential equations.' Numerical Algorithms

About Benedict Leimkuhler (University of Leicester)

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.

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.

Additional information

NPB9780521772907
9780521772907
0521772907
Simulating Hamiltonian Dynamics by Benedict Leimkuhler (University of Leicester)
New
Hardback
Cambridge University Press
2005-02-14
396
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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Customer Reviews - Simulating Hamiltonian Dynamics