Fall 2008, Math 676, Section
1
Spectral
Methods
Class Time & Room
Tue.Thu. 9:30-10:45am, Engrg E202
Instructor: Prof. Jiangguo (James) Liu
Office: Weber 127
Phone: (970)491-3067
Email: liu@math.colostate.edu
URL: http://www.math.colostate.edu/~liu/
Office Hour: MWF
11am--12pm and by
appointment
Spectral methods, along with finite difference and finite element
methods, are the "Big Three" technologies for numerical solutions of
differential equations. Spectral methods are well known for their
high order accuracy and have been widely used in fluid mechanics,
linear and nonlinear waves, and many other problems arising from
mathematics and engineering.
In this graduate topic course, we will study development, convergence,
stability, and implementations of the spectral methods. These
include spectral Galerkin methods, pseudospectral (collocation)
methods, and fast transforms; applications to steady-state and
time-dependent problems; and the spectral methods for discontinuous
problems and general grids.
Course
grades
based on participation in class discussions and performance on assigned
projects.
Textbook
We don't have a textbook for this topic course, but the following
references will be very helpful.
[1] J.Boyd, Chebyshev and Fourier Spectral Methods, Dover, 2001.
[2] C.Canuto, M.Y.Hussaini, A.Quarteroni, and T.A.Zang, Spectral
Methods, Springer, 2006.
[3] D.Gottlieb and S.Orszag, Numerical Analysis of Spectral Methods,
SIAM, 1977.
[4] J.Hesthaven, S.Gottlieb, and D.Gottlieb, Spectral Methods for
Time-Dependent Problems, Cambridge University Press,
2007.
[5] L.Trefethen, Spectral Methods in Matlab, SIAM, 2000.
Last modified by
J.Liu on Mon. 05/12/2008