Description

This is a gradute special topics course whose contents include:

1. Symplectic integration (Introduction to Lagrangian and Hamiltonian mechanics, Noether's theorem, geometric formulation of Hamiltonian mechanics, symplectic integrators for ODEs)
2. Variational integrators (Geometric formulation of Lagrangian mechanics, discrete Lagrangian mechanics, numerical and geometric properties of variational integrators)
3. Invariant discretization (Introduction to Lie groups and Lie algebras, symmetries of differential equations, moving frames and invariants, invariant discretization of ODEs and PDEs)
4. Conservative discretization (Conservation laws and first integrals, projection methods, discrete gradient methods, multiplier methods for ODEs)

Prerequisites

Undergraduate advanced calculus, linear algebra, a solid course in numerical analysis, a programming course (preferably knowledge of Matlab)

Recommended text

• Geometric numerical integration, E. Hairer, C. Lubich and G. Wanner (Springer, 2006)