Spectral methods based on prolate spheroidal wave functions for hyperbolic PDEs

We examine the merits of using prolate spheroidal wave functions (PSWFs) as basis functions when solving hyperbolic PDEs using pseudospectral methods. The relevant approximation theory is reviewed and some new approximation results in Sobolev spaces are established. An optimal choice of the band-limit parameter for PSWFs is derived for single-mode functions. Our conclusion is that one might gain from using the PSWFs over the traditional Chebyshev or Legendre methods in terms of accuracy and efficiency for marginally resolved broadband solutions.


Published in:
SIAM Journal on Numerical Analysis, 43, 5, 1912-1933
Year:
2005
Publisher:
Society for Industrial and Applied Mathematics
ISSN:
0036-1429
Keywords:
Laboratories:




 Record created 2013-11-12, last modified 2018-09-13

Publisher's version:
Download fulltext
PDF

Rate this document:

Rate this document:
1
2
3
 
(Not yet reviewed)