Symplectic Geometric Algorithms for Hamiltonian Systems

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Springer Science & Business Media, Oct 18, 2010 - Mathematics - 676 pages

"Symplectic Geometric Algorithms for Hamiltonian Systems" will be useful not only for numerical analysts, but also for those in theoretical physics, computational chemistry, celestial mechanics, etc. The book generalizes and develops the generating function and Hamilton-Jacobi equation theory from the perspective of the symplectic geometry and symplectic algebra. It will be a useful resource for engineers and scientists in the fields of quantum theory, astrophysics, atomic and molecular dynamics, climate prediction, oil exploration, etc. Therefore a systematic research and development of numerical methodology for Hamiltonian systems is well motivated. Were it successful, it would imply wide-ranging applications.

 

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Contents

Introduction
1
Chapter 1 Preliminaries of Differentiable Manifolds
39
Chapter 2 Symplectic Algebra and Geometry Preliminaries
113
Chapter 3 Hamiltonian Mechanics and Symplectic Geometry
165
Chapter 4 Symplectic Difference Schemes for Hamiltonian Systems
187
Chapter 5 The Generating Function Method
213
Chapter 6 The Calculus of Generating Functions and Formal Energy
248
Chapter 7 Symplectic RungeKutta Methods
277
Chapter 10 VolumePreserving Methods for SourceFree Systems
443
Chapter 11 Contact Algorithms for Contact Dynamical Systems
477
Chapter 12 Poisson Bracket and LiePoisson Schemes
498
Chapter 13 KAM Theorem of Symplectic Algorithms
549
Chapter 14 LeeVariational Integrator
581
Chapter 15 Structure Preserving Schemes for Birkhoff Systems
617
Chapter 16 Multisymplectic and Variational Integrators
641
Symbol
662

Chapter 8 Composition Scheme
365
Chapter 9 Formal Power Series and BSeries
407

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