Numerical Methods for Partial Differential Equations I: Finite Difference Methods for Time-Dependent PDEs

Textbook: B. Gustafsoon, H.-O. Kreiss and J. Oliger, Time Dependent Problems and Difference Methods, John Wiley & Sons, Inc., 1995.

Description: This course is centered around the development and analysis of finite difference methods for the solution of time-dependent partial differential equations (PDEs). The main focus is on the analysis of initial value problems (Part I of the textbook), including Fourier analysis of difference methods, well-posedness of scalar equations and systems of equations, and stability and convergence theory of hyperbolic and parabolic type problems. It will also cover the method-of-lines approach, the associated semi-discrete analysis and finite volume formulations.

Prerequisite: Some basic programming skills are required as well as basic knowledge about PDEs and Fourier analysis.

Homework: Weekly homework is required; late homework will be discounted by 50%. Both theory and computations are included in the problems sets.

Exams: One midterm exam (in class; open books) and one take-home final exam.

Grading: The final grade will be determined based on homework (30%), midterm (30%) and final (40%).