Numerical Solution of Ordinary Differential Equations: IVP Problems and PDE Related Issues

Catalog description

The course seeks to lay the foundation for the development and analysis of numerical methods for solving systems of ordinary differential equations. With a dual emphasis on analysis and efficient implementations, we shall develop the theory for multistage methods (Runge-Kutta type) and multi-step methods (Adams/BDF methods). The discussion includes definitions of different notions of stability, stiffness and stability regions, global/local error estimation, and error control. We also discuss more specialized topics such as symplectic integration methods, parallel-in-time methods, include splitting methods, methods for differential-algebraic equations (DAE), deferred correction methods, and order reduction problems for IBVP, TVD and IMEX methods.