Math 517 Finite Difference Methods

Fall 2004@ISU

Course Description: a course focusing on the study of mathematical tools that are essential in developing, analyzing, and successfully using Finite Difference Methods for time-dependent problems, particularly for problems involving shock waves and singular layers. Mathematical structures of underlying equations and their solutions are discussed before numerical methods are introduced.
Topics to be covered in Math 517
- Time-dependent PDES --- derivation of conservation laws, physical models, shock waves, Riemann problems ...
- Numerical Methods for linear problems ---model equations; truncation error, stability, convergence, ...
- Numerical Methods for nonlinear problems--- consistency, conservative, ...
- Godunov'type schemes --- central schemes, upwind schemes, approximate Riemann solvers...
- High-resolution methods --- flux limiter, slope limiter ...
- Semi-discrete methods ---ENO, spatial reconstruction ...
- Nonlinear stability --- TVD, TVB, monotonicity...
References:    --- Numerical Methods for Conservation Laws, Birkaeuser1992.
                                 by Randall Leveque
                           --- Time-dependent Problems and Difference Methods, Wiley 1995.
                                 by Bertil Gustafsson, Heinz-Otto Kreiss and Joseph Oliger

Assignments will be made by topic; Click here to get an up-to-date list of homework assignments.

Prior announcement will be made if certain assignment needs to be collected for grading.

Homework assignments consist of both theoretical and computational work.

For the computational assignments, you are encouraged to use Matlab.

Examinations: There will be an in-class midterm and one take-home final project.

Grading Policy: Homework: 30%+ Midterm: 30% + Final: 40%. An appropriate scaling may be applied at the end of the semester to determine the final grade.