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＜電子ブック＞
Symplectic Geometric Algorithms for Hamiltonian Systems / by Kang Feng, Mengzhao Qin

版	1st ed. 2010.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2010
本文言語	英語
大きさ	XXIII, 676 p : online resource
著者標目	*Feng, Kang author Qin, Mengzhao author SpringerLink (Online service)
件　名	LCSH:Geometry, Differential LCSH:Algebraic topology LCSH:Mathematics -- Data processing  全ての件名で検索 LCSH:Geometry LCSH:Quantum physics LCSH:Fluid mechanics FREE:Differential Geometry FREE:Algebraic Topology FREE:Computational Mathematics and Numerical Analysis FREE:Geometry FREE:Quantum Physics FREE:Engineering Fluid Dynamics
一般注記	Preliminaries of Differentiable Manifolds -- Symplectic Algebra and Geometry Preliminaries -- Hamiltonian Mechanics and Symplectic Geometry -- Symplectic Difference Schemes for Hamiltonian Systems -- The Generating Function Method -- The Calculus of Generating Functions and Formal Energy -- Symplectic Runge-Kutta Methods -- Composition Scheme -- Formal Power Series and B-Series -- Volume-Preserving Methods for Source-Free Systems -- Contact Algorithms for Contact Dynamical Systems -- Poisson Bracket and Lie-Poisson Schemes -- KAM Theorem of Symplectic Algorithms -- Lee-Variational Integrator -- Structure Preserving Schemes for Birkhoff Systems -- Multisymplectic and Variational Integrators "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 HTTP:URL=https://doi.org/10.1007/978-3-642-01777-3

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