Math 517 Finite Difference Methods
Spring
2010@ISU
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Instructor: Hailiang Liu
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Time and Location: TR 11:00AM -12:20PM; Carver Hall 0032
- Outline: Topic outline for Math 517.
- 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. Mathematical structures of underlying equations and their solutions are
discussed before numerical methods are introduced.
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Topics to be covered in Math 517
- Time-dependent PDES --- derivation of equations, physical
backgrounds ...
- Numerical Methods for linear problems --- model equations; truncation error,
stability, convergence...
- Numerical Methods for nonlinear problems --- consistency, conservative, ...
- Godunov'type schemes --- symmetric schemes, upwind schemes, approximate Riemann solvers ...
- High-resolution methods --- high resolution reconstruction ...
- Semi-discrete methods --- Spatial reconstruction ...
- Nonlinear stability --- TVD, monotonicity...
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Reference Texts:
- Time-dependent Problems and Difference Methods, Wiley 1995 by Bertil Gustafsson, Heinz-Otto Kreiss and Joseph Oliger
- Numerical Methods for Conservation Laws, Birkaeuser1992. by Randall Leveque
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Homework Assignments: 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.
I will clarify a few days ahead of time what topics will be covered on each
exam.
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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.