Symplectic Geometric Algorithms for Hamiltonian Systems

1. Introduction
Kang Feng, Mengzhao Qin

2. Preliminaries of Differentiable Manifolds
Kang Feng, Mengzhao Qin

3. Symplectic Algebra and Geometry Preliminaries
Kang Feng, Mengzhao Qin

4. Hamiltonian Mechanics and Symplectic Geometry
Kang Feng, Mengzhao Qin

5. Symplectic Difference Schemes for Hamiltonian Systems
Kang Feng, Mengzhao Qin

6. The Generating Function Method
Kang Feng, Mengzhao Qin

7. The Calculus of Generating Functions and Formal Energy
Kang Feng, Mengzhao Qin

8. Symplectic Runge-Kutta Methods
Kang Feng, Mengzhao Qin

9. Composition Scheme
Kang Feng, Mengzhao Qin

10. Formal Power Series and B-Series
Kang Feng, Mengzhao Qin

11. Volume-Preserving Methods for Source-Free Systems
Kang Feng, Mengzhao Qin

12. Contact Algorithms for Contact Dynamical Systems
Kang Feng, Mengzhao Qin

13. Poisson Bracket and Lie-Poisson Schemes
Kang Feng, Mengzhao Qin

14. KAM Theorem of Symplectic Algorithms
Kang Feng, Mengzhao Qin

15. Lee-Variational Integrator
Kang Feng, Mengzhao Qin

16. Structure Preserving Schemes for Birkhoff Systems
Kang Feng, Mengzhao Qin

17. Multisymplectic and Variational Integrators
Kang Feng, Mengzhao Qin

Keywords: Mathematics, Computational Mathematics and Numerical Analysis, Geometry, Algebraic Topology, Quantum Physics, Engineering Fluid Dynamics