This advanced text explores a category of mathematical problems that occur frequently in physics and other sciences. Five preliminary chapters make the book accessible to students without extensive background in this area. Topics include Hamiltonian systems, symplecticness, numerical methods, order conditions, and implementation.
The heart of the book, chapters 6 through 10, explores symplectic integration, symplectic order conditions, available symplectic methods, numerical experiments, and properties of symplectic integrators. The final four chapters contain more advanced material: generating functions, Lie formalism, high-order methods, and extensions. Many numerical examples appear throughout the text.

Preface

1. Hamiltonian systems

2. Symplecticness

3. Numerical methods

4. Order conditions

5. Implementation

6. Symplectic integration

7. Symplectic order conditions

8. Available symplectic methods

9. Numerical experiments

10. Properties of symplectic integrators

11. Generating functions

12. Lie formalism

13. High-order methods

14. Extensions

References

Symbol index

Index