Analysis and implementation of numerical methods for initial and two point boundary value problems for ordinary differential equations.
- Review of Ordinary Differential Equations - Initial and boundary value problems, existence and uniqueness, regularity, stability
- Initial Value Problems - Single and multistep methods, explicit and implicit methods, fixed point and Newton's methods, error and stability, stiff problems
- Boundary Value Problems - Collocation and finite element methods, fixed point and Newton's methods, error and stability
- Mesh Selection - Error estimation, efficient computation