ANALYSIS OF SPECTRAL APPROXIMATIONS USING PROLATE SPHEROIDAL WAVE FUNCTIONS

被引：0
|
作者：
Wang, Li-Lian [1 ]
机构：
[1] Nanyang Technol Univ, Div Math Sci, Sch Phys & Math Sci, Singapore 637371, Singapore
来源：
MATHEMATICS OF COMPUTATION | 2010年 / 79卷 / 270期
关键词：
Prolate spheroidal wave functions; bandlimited functions; approximations in Sobolev spaces; spectral methods; quasi-uniform grids; DIFFERENTIATION; QUADRATURE; ELEMENT;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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页码：807 / 827
页数：21
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