Spectral Methods Based on Prolate Spheroidal Wave Functions for Hyperbolic PDEsSIAM Journal on Numerical Analysis (2006)
AbstractWe 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.
Publication DateJuly 25, 2006
Citation InformationQian-Yong Chen, D. Gottlieb and J. S. Hesthaven. "Spectral Methods Based on Prolate Spheroidal Wave Functions for Hyperbolic PDEs" SIAM Journal on Numerical Analysis Vol. 43 Iss. 5 (2006)
Available at: http://works.bepress.com/qian_yong_chen/1/