Simulating Hamiltonian Dynamics

Released on by Benedict Leimkuhler
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  • Simulating Hamiltonian Dynamics Book Detail

  • Author : Benedict Leimkuhler
  • Release Date : 2004
  • Publisher : Cambridge University Press
  • Genre : Mathematics
  • Pages : 464
  • ISBN 13 : 9780521772907
  • File Size : 96,96 MB
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Simulating Hamiltonian Dynamics by Benedict Leimkuhler PDF Summary

Book Description: 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.

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This is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics a