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© 2010

Symplectic Geometric Algorithms for Hamiltonian Systems

Book

Table of contents

  1. Front Matter
    Pages i-xxiii
  2. Kang Feng, Mengzhao Qin
    Pages 1-38
  3. Kang Feng, Mengzhao Qin
    Pages 39-112
  4. Kang Feng, Mengzhao Qin
    Pages 113-164
  5. Kang Feng, Mengzhao Qin
    Pages 165-186
  6. Kang Feng, Mengzhao Qin
    Pages 187-211
  7. Kang Feng, Mengzhao Qin
    Pages 213-247
  8. Kang Feng, Mengzhao Qin
    Pages 249-275
  9. Kang Feng, Mengzhao Qin
    Pages 277-364
  10. Kang Feng, Mengzhao Qin
    Pages 365-406
  11. Kang Feng, Mengzhao Qin
    Pages 407-442
  12. Kang Feng, Mengzhao Qin
    Pages 443-476
  13. Kang Feng, Mengzhao Qin
    Pages 477-497
  14. Kang Feng, Mengzhao Qin
    Pages 499-548
  15. Kang Feng, Mengzhao Qin
    Pages 549-580
  16. Kang Feng, Mengzhao Qin
    Pages 581-616
  17. Kang Feng, Mengzhao Qin
    Pages 617-639
  18. Kang Feng, Mengzhao Qin
    Pages 641-661
  19. Back Matter
    Pages 663-676

About this book

Introduction

"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.

Keywords

Contact systems Generating function Lie– Poisson systems Symplectic geometry Theoretical physics ZSTPH algorithms manifold

Authors and affiliations

  1. 1.Institute of Computational Mathematics and Scientific/Engineering ComputingBeijingChina

Bibliographic information

Reviews

From the reviews:

“This book is about the construction of numerical algorithms that preserve geometric properties and physical principles associated with ordinary differential systems. … the book provides a comprehensive overview of geometric numerical integration of Hamiltonian systems, also offering some of the outstanding results achieved by the authors, making this monograph a valuable contribution to the bibliography in this field that will be of interest to a wide range of researchers in a variety of areas.” (A. San Miguel, Mathematical Reviews, Issue 2012 h)