Math 545 Term Project
Your term project will explore a topic relevant to the numerical
solution of differential equations of evolution. See the list below
for some suggestions. A good project will
have a numerical component and an analysis component. Your project
may also include an in-class presentation. This is optional.
Your report should be type set using LaTeX or your favorite
technology. (Please don't just copy verbatim from whatever sources you
used. That would be plagiarism.) It is due on the last day of class.
If you turn it in significantly before the end of the semester, I will
mark it as soon as I can and return it to you. You will then have the
option of turning in an improved version.
Project Topic Suggestions (to be updated periodically)
For most of these topics you will be able to start out in the text
but will ultimately have to go to the literature.
Linear Difference equations and the Jordan canonical form (D.2.1)
Dahlquist's theorem: consistency + zero-stability = convergence (6.4,
order stars, limits on the order of A-stable methods. (7.7)
Runge-Kutta-Chebyshev method (8.6)
- MOL with discretization in space by a spectral method
Locally one-dimensional method (9.8, 9.8.1)
Alternating-Direction implicit method (9.8.2)
Any of the topics listed in (9.9 Other discretizations)
Beam-Warming method (10.4.2), accuracy, stability, performance
Dispersion: phase velocity vs. group velocity (10.9, Appendix E.3)
Anything from Chapter 11
Something related to your research
Some other topic of your choosing
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