2010

Symplectic Geometric Algorithms for Hamiltonian Systems

Authors:

ISBN: 978-3-642-01776-6 (Print) 978-3-642-01777-3 (Online)

Table of contents (17 chapters)

  1. Front Matter

    Pages i-xxiii

  2. No Access

    Book Chapter

    Pages 1-38

    Introduction

  3. No Access

    Book Chapter

    Pages 39-112

    Preliminaries of Differentiable Manifolds

  4. No Access

    Book Chapter

    Pages 113-164

    Symplectic Algebra and Geometry Preliminaries

  5. No Access

    Book Chapter

    Pages 165-186

    Hamiltonian Mechanics and Symplectic Geometry

  6. No Access

    Book Chapter

    Pages 187-211

    Symplectic Difference Schemes for Hamiltonian Systems

  7. No Access

    Book Chapter

    Pages 213-247

    The Generating Function Method

  8. No Access

    Book Chapter

    Pages 249-275

    The Calculus of Generating Functions and Formal Energy

  9. No Access

    Book Chapter

    Pages 277-364

    Symplectic Runge-Kutta Methods

  10. No Access

    Book Chapter

    Pages 365-406

    Composition Scheme

  11. No Access

    Book Chapter

    Pages 407-442

    Formal Power Series and B-Series

  12. No Access

    Book Chapter

    Pages 443-476

    Volume-Preserving Methods for Source-Free Systems

  13. No Access

    Book Chapter

    Pages 477-497

    Contact Algorithms for Contact Dynamical Systems

  14. No Access

    Book Chapter

    Pages 499-548

    Poisson Bracket and Lie-Poisson Schemes

  15. No Access

    Book Chapter

    Pages 549-580

    KAM Theorem of Symplectic Algorithms

  16. No Access

    Book Chapter

    Pages 581-616

    Lee-Variational Integrator

  17. No Access

    Book Chapter

    Pages 617-639

    Structure Preserving Schemes for Birkhoff Systems

  18. No Access

    Book Chapter

    Pages 641-661

    Multisymplectic and Variational Integrators

  19. Back Matter

    Pages 663-676