Symplectic Geometric Algorithms for Hamiltonian Systems

• Main Authors: Feng, Kang. (Author), Qin, Mengzhao. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2010.
• Subjects: Mathematics.; Computer science > Mathematics.; Geometry.; Algebraic topology.; Quantum theory.; Hydraulic engineering.; Computational Mathematics and Numerical Analysis.; Algebraic Topology.; Quantum Physics.; Engineering Fluid Dynamics.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-01777-3

"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 the...

Table of Contents:

• Preliminaries of Differential 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 Function and Formal Energy
• Symplectic Runge-Kutta Methods
• Composition Scheme
• Formal Power Series and B-Series
• Volume-Preserving Methods for Source-Free Systems
• Free Systems
• Contact Algorithms for Contact Dynamic 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.����.