Math 517 Finite Difference Methods
Lectures: TR 12:40PM -2:00PM, Carver
- 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,
- Godunov'type schemes --- central schemes, upwind schemes, approximate
- 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
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
For the computational assignments, you are
encouraged to use Matlab.
Examinations: There will be an
in-class midterm and
one take-home final project. Exam problems will be
similar to homework assignments.
I will clarify a few days ahead of time what topics will be covered on each
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.