An improved estimate of PSWF approximation and approximation by Mathieu functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:379

Article

Wang, Li-Lian¹  Zhang, Jing¹ 

[1] Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637371, Singapore

关键词: Prolate spheroidal wave functions;    Mathieu functions;    Spectral approximation;    Order of convergence;   

DOI  :  10.1016/j.jmaa.2010.12.024

来源: Elsevier

【 摘 要 】

In this paper, an error estimate of spectral approximations by prolate spheroidal wave functions (PSWFs) with explicit dependence on the bandwidth parameter and optimal order of convergence is derived, which improves the existing result in [Chen et al., Spectral methods based on prolate spheroidal wave functions for hyperbolic PDEs, SIAM J. Numer. Anal. 43 (5) (2005) 1912-1933]. The underlying argument is applied to analyze spectral approximations of periodic functions by Mathieu functions, which leads to new estimates featured with explicit dependence on the intrinsic parameter. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free