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.
SIAM J. Numer. Anal 2005 Chen.pdf
Publisher's Version
http://purl.org/coar/version/c_970fb48d4fbd8a85
openaccess
435.93 KB
Adobe PDF
30f54a51068a7326ad39bdf7e25f9b68