ACM Transactions on Mathematical Software (TOMS)
Algorithm 899: The Matlab postprocessing toolkit
ACM Transactions on Mathematical Software (TOMS)
A Prolate-Element Method for Nonlinear PDEs on the Sphere
Journal of Scientific Computing
The Nonconvergence of $$h$$h-Refinement in Prolate Elements
Journal of Scientific Computing
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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.