Numerical Partial Differential Equations -
Pseudospectral and Radial Basis Function Methods
Math 667 (may be taken as Math 480 for
undergraduate credit)
About the class: The class is a
first course on the numerical solution of partial differential
equations. Local (finite difference) and global
(pseudospectral) polynomial based methods and local and global
Radial Basis Function (RBF) based methods for the numerical solution
of steady and time-dependent Partial Differential Equations (PDEs)
will be developed and analyzed. The class will be project
based and will expose students to active research areas in the field
of numerical PDEs.
Prerequisites: MTH 335
(Differential Equations) and computer programming experience.
Text: Spectral
Methods in MATLAB, ISBN-13: 978-0898714654
Supplemental
reading:
- Numerical
Analysis (the text for Math 443/643), 2nd edition,
ISBN-13: 978-0321783677
- Multiquadric
Radial Basis Function Approximation Methods for the Numerical
Solution of Partial Differential Equations. Advances
in Computational Mechanics, volume 2, 2009. ISSN:
1940-5820. (pdf)
Applets
- ODE Lab -
illustrates properities of numerical methods for ODE initial
value problems
- Numerical
Advection - solves the 1d and advection equation with
periodic boundary conditions using a large number of different
numerical methods.
- Removal
of Gibbs' oscillations - illustrates post-processing
methods to remove Gibbs' oscillations from Fourier and Chebyshev
approximations of functions that have discontinuities.