A comparative study of meshless complex quadrature rules for highly oscillatory integrals. (March 2015)

• Record Type: Journal Article
• Authors: Siraj-ul-Islam, ; Nasib, Uzma
• Is Part Of: Engineering analysis with boundary elements. Volume 52(2015:Mar.)
• Page Start: 71
• Page End: 80
• Publication Date: 2015-03
• Subjects: Meshless method -- Oscillatory integral -- Levin׳s method -- Shape parameter -- Condition number -- Radial Basis function -- Bessel RBF -- Thin plate spline; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2014.11.024
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: In this paper a stable and modified form of the Levin method based on Bessel radial basis functions is employed for numerical solution of highly oscillatory integrals. In the proposed technique, the multiquadric radial basis function (Levin, 1982[1] ; Siraj-ul-Islam et al., 2013[2] ) is replaced by Bessel radial basis functions (Fornberg et al., 2006[3] ) and thin plate spline of order three. In this scheme the integration form is first transformed into differential form and then the numerical solution of the corresponding differential form is found. The accuracy and the algebraic stability in the form of well-conditioned coefficient matrices of the proposed methods are confirmed through numerical experiments.