Analysis of spectral approximations using prolate spheroidal wave functions

Abstract. In this paper, the approximation properties of the prolate spheroidal wave functions of order zero (PSWFs) are studied, and a set of optimal error estimates are derived for the PSWF approximation of non-periodic functions in Sobolev spaces. These results serve as an indispensable tool for the analysis of PSWF spectral methods. A PSWF spectral-Galerkin method is proposed and analyzed for elliptic-type equations. Illustrative numerical results consistent with the theoretical analysis are also presented.

• Type: Journal
• Year: 2010
• Where: MOC
• Authors: Li-lian Wang
• Keywords: MOC 2010, Optimal Error Estimates, Prolate Spheroidal Wave Functions, PSWF Spectral Methods, Security Privacy