A comparative study of meshless complex quadrature rules for highly oscillatory integrals

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.