An improved estimate of PSWF approximation and approximation by Mathieu functions

作者：Wang Li Lian^*; Zhang Jing

来源：Journal of Mathematical Analysis and Applications, 2011, 379(1): 35-47.

DOI：10.1016/j.jmaa.2010.12.024

• Prolate spheroidal wave functions
• Mathieu functions
• Spectral approximation
• Order of convergence

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.

• 出版日期2011-7-1
• 单位南阳理工学院