Computing Highly Oscillatory Integrals : Back Matter Page 1 Bibliography [1] M. Abramowitz
and IA Stegun. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical …

The present paper is dedicated to a variational method for the construction of optimal
quadrature formulas in the sense of Sard in the Hilbert space W˜ 2 (m, m− 1) of complex …

Steepest descent methods combining complex contour deformation with numerical
quadrature provide an efficient and accurate approach for the evaluation of highly oscillatory …

The discrete ordinate method for the transfer of monochromatic unpolarized radiation in non-
isothermal, vertically inhomogeneous media, as implemented in the computer code Discrete …

Abstract Modified Gauss–Laguerre exponentially fitted quadrature rules are introduced for
the computation of integrals of oscillatory functions over the whole positive semiaxis. Their …

In this paper we present a unified framework for asymptotic analysis of the finite Hankel
transform. This framework enables us to derive asymptotic expansions of the transform …

In this paper, augmented Levin methods are proposed for the computation of oscillatory
integrals with stationary points and an algebraically or logarithmically singular kernel …

This paper provides a product integration rule for highly oscillating integrands of the type∫−
aae− i ω (x− y) f (x) dx, a> 0, i=− 1, y∈[− a, a], ω∈ R+, based on the approximation of f by …

We propose a new method for the efficient approximation of a class of highly oscillatory
weighted integrals where the oscillatory function depends on the frequency parameter ω≥ …

We consider polynomials pn ω (x) that are orthogonal with respect to the oscillatory weight w
(x)= ei ω x on [− 1, 1], where ω> 0 is a real parameter. A first analysis of pn ω (x) for large …