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. The symplectic geometric algorithm of K. Feng is unique Classical, fundamental, and important reference in structure-preserving algorithmof computational mathematics A must for the computational mathematician to understand the background, motivation, and the significance of the symplectic geometric algorithm INDICE: Preliminaries of Differential Manifolds.- Symplectic Algebra and Geometry Preliminaries.- Hamiltonian Mechanics and Symplectic Geometry.- Symplectic Difference Schemes for Hamiltonian Systems.- General Theory for Construction of Symplectic Schemes of Hamiltonian Systems.- Calculus of Generating Function and Formal Energy Hamiltonian Algorithm.- Symplectic Runge-Kutta Methods.- Composition Scheme.- Formal Power Series.- Volume-Preserving Schemes for Source-Free Systems.- Contact Algorithms for Contact Dynamic Systems.- Poisson Bracket and Lie-Poisson Bracket.
- ISBN: 978-3-642-01776-6
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 640
- Fecha Publicación: 01/11/2009
- Nº Volúmenes: 1
- Idioma: Inglés