Eigenfunctions of the Airy's integral transform: Properties, numerical computations and asymptotic behaviors

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:389

Article

Karoui, Abderrazek¹  Mehrzi, Issam¹  Moumni, Taher¹ 

[1] Univ Carthage, Dept Math, Fac Sci Bizerte, Jarzouna 7021, Tunisia

关键词: Airy's function;    Airy's integral transform;    Eigenfunctions and eigenvalues;    Gaussian quadrature method;    WKB method;    Asymptotic behaviors;   

DOI  :  10.1016/j.jmaa.2011.12.036

来源: Elsevier

【 摘 要 】

This paper is devoted to the study of the spectrum of the integral operator with Airy's kernel. We provide the reader with some efficient methods of computing the eigenfunctions and the eigenvalues of this operator. The first method is based on the use of a differential operator which commutes with this integral operator. The second method is based on a Gaussian quadrature method applied to the finite Airy's transform. The asymptotic behavior of the eigenfunctions is studied by the use of a WKB method. Some numerical examples are given to illustrate results of this work. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free