The efficient and accurate calculation of integrals, especially singular and nearly singular
integrals, poses a great challenge in boundary integral equation (BIE) methods. In this …

We present a generalised bivariate Filon–Clenshaw–Curtis cubature for the double highly
oscillatory integrals on the square. Under the Hermite interpolatory conditions meeting an …

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 …

A boundary point interpolation method (BPIM) is presented in this paper for numerical
solving acoustic problems. The BPIM is a boundary-type meshless method that combines …

Abstract The Filon–Clenshaw–Curtis method (FCC) for the computation of highly oscillatory
integrals is known to attain surprisingly high precision. Yet, for large values of frequency ω ω …

In this paper, we aim to derive some error bounds for Filon-Clenshaw-Curtis quadrature for
highly oscillatory integrals. Thanks to the asymptotics of the coefficients in the Chebyshev …

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 …

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 …

We investigate the impact of adding inner nodes for a Filon-type method for highly oscillatory
quadrature. The error of Filon-type method is composed of asymptotic and interpolation …

In this paper, we present the Clenshaw–Curtis–Filon methods and the higher order methods
for computing many classes of oscillatory integrals with algebraic or logarithmic singularities …