Two types of splitting algorithms are proposed for approximation of Cauchy type singular
integrals having high frequency Fourier kernel. To evaluate non-singular integrals, modified …

In this article, we present and analyze efficient methods for computing the Cauchy principal
value integral of the oscillatory Bessel function∫ abf (x) x− c J m (ω x) dx, where 0≤ a< c< b …

For the finite Hilbert transform of oscillatory functions Q (f; c, ω)=−∫− 1 1 f (x) ei ω x∕(x− c)
dt with a smooth function f and real ω≠ 0, for c∈(− 1, 1) in the sense of Cauchy principal …

In this paper, we first propose different combination methods to compute the Cauchy
principal value integrals of oscillatory Bessel functions. By special transformations, the …

Abstract The Clenshaw–Curtis-type quadrature rule is proposed for the numerical evaluation
of the hypersingular integrals with highly oscillatory kernels and weak singularities at the …

A new interpolatory-type quadrature rule is proposed for the numerical evaluation of Cauchy
principal value integrals of oscillatory kind⨍− 1 1 f (x) x− τ ei ω xdx, where τ∈(− 1, 1). The …

In this paper, new uniform approximation schemes for computation of hypersingular finite-
part integrals are studied. The methods are verified to be supremely qualified for oscillatory …

In this paper, we study the asymptotics and fast computation of the one-sided oscillatory
Hilbert transforms of the form H^+(f (t) e^ i ω t)(x)=-\!\!\!\!\!\! ∫\nolimits _\!\!\! 0^ ∞ e^ i ω tf (t) …

Abstract Based on the Filon–Clenshaw–Curtis method for highly oscillatory integrals, and
together with the Sommariva's result (Sommariva, 2013) for Clenshaw–Curtis quadrature …

A new automatic quadrature scheme is proposed for evaluating Cauchy principal value
integrals of oscillatory functions:⨍-11f (x) exp (iωx)(x-τ)-1dx (-1< τ< 1, ω∈ R). The desired …