Numerical Hamiltonian Problems

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.

J. M. Sanz-Serna is on the faculty of Charles III University of Madrid.
M. P. Calvo teaches at the University of Valladolid.

Preface1. Hamiltonian systems2. Symplecticness3. Numerical methods4. Order conditions5. Implementation6. Symplectic integration7. Symplectic order conditions8. Available symplectic methods9. Numerical experiments10. Properties of symplectic integrators11. Generating functions12. Lie formalism13. High-order methods14. ExtensionsReferencesSymbol indexIndex