We present a simple discretization scheme for the hypersingular integral representa-tion of
the fractional Laplace operator and solver for the corresponding fractional Laplacian …

In this work, a finite difference method of tunable accuracy for fractional differential equations
(FDEs) with end-point singularities is developed. Modified weighted shifted Grünwald …

The manuscript describes a quadrature rule that is designed for the high order discretization
of boundary integral equations (BIEs) using the Nyström method. The technique is designed …

We present a simple, accurate method for computing singular or nearly singular integrals on
a smooth, closed surface, such as layer potentials for harmonic functions evaluated at points …

This paper describes a locally corrected trapezoidal quadrature method for the discretization
of singular and hypersingular boundary integral operators (BIOs) that arise in solving …

We present a framework using the Quantized Tensor Train (qtt) decomposition to accurately
and efficiently solve volume and boundary integral equations in three dimensions. We …

We introduce a numerical method based on an integral equation formulation for simulating
drops in viscous fluids in the plane. It builds upon the method introduced by Kropinski in …

A high-order accurate quadrature rule for the discretization of boundary integral equations
(BIEs) on closed smooth contours in the plane is introduced. This quadrature can be viewed …

We present new higher-order quadratures for a family of boundary integral operators re-
derived using the approach introduced in Kublik et al.(2013)[7]. In this formulation, a …

We present a family of high-order trapezoidal rule-based quadratures for a class of singular
integrals, where the integrand has a point singularity. The singular part of the integrand is …