Quadrature Methods for Highly Oscillatory Singular Integrals

Abstract

The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.

Levin methods for highly oscillatory integrals with singularities

“…A significant amount of work has also been done on the computation of singular and oscillatory integrals of the type (1.1). The asymptotic behavior for the integral was obtained by repeated integration by parts [8,9] or by the inverse functions [21]. When the oscillator is linear, i.e., g(x) = x, it was studied by the Clenshaw-Curtis-Filon-type methods [17,18,34], in which the modified moments can be obtained numerically by stable recurrence relations.…”

“…In the following, we consider the asymptotic order of the new Levin method. To this end, we recall a lemma concluded from the results in [34] and [9].…”