Spectral methods based on prolate spheroidal wave functions for hyperbolic PDEs

• Published in: SIAM Journal on Numerical Analysis (ISSN: 0036-1429), vol. 43, num. 5, p. 1912-1933
• Society for Industrial and Applied Mathematics, 2005

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.

Keywords: prolate spheroidal wave functions ; spectral methods ; penalty methods

Reference

• EPFL-ARTICLE-190376
• doi:10.1137/S0036142903432425
• View record in Web of Science

Record created on 2013-11-12, modified on 2017-05-12