Related papers: Singular integration towards a spectrally accurate…
This paper introduces a high-order-accurate strategy for integration of singular kernels and edge-singular integral densities that appear in the context of boundary integral equation formulations of the problem of acoustic scattering. In…
We consider the linear integro-differential operator $L$ defined by \[ Lu(x) =\int_\Rn (u(x+y) - u(x) - 1_{[1,2]}(\alpha) 1_{\{|y|\leq 2\}}(y)y \cdot \nabla u(x)) k(x,y) \sd y . \] Here the kernel $k(x,y)$ behaves like $|y|^{-d-\alpha}$,…
We revisit the classical kernel method of approximation/interpolation theory in a very specific context motivated by the desire to obtain a robust procedure to approximate discrete data sets by (super)level sets of functions that are merely…
We perform a numerical approximation of coherent sets in finite-dimensional smooth dynamical systems by computing singular vectors of the transfer operator for a stochastically perturbed flow. This operator is obtained by solution of a…
We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a…
This work aims to construct an efficient and highly accurate numerical method to address the time singularity at $t=0$ involved in a class of time-fractional parabolic integro-partial differential equations in one and two dimensions. The…
We consider fully nonlinear elliptic integro-differential operators with kernels of variable orders, which generalize the integro-differential operators of the fractional Laplacian type in \cite{CS}. Since the order of differentiability of…
A development of an inverse first-order divided difference operator for functions of several variables is presented. Two generalized derivative-free algorithms builded up from Ostrowski's method for solving systems of nonlinear equations…
A simple but successful strategy for building a discrete diffusion operator in finite volume schemes of industrial use is to correct the standard two-point flux approximation with a term accounting for the local mesh non-orthogonality.…
We show how a rescaling of fractional operators with bounded kernels may help circumvent their documented deficiencies, for example, the inconsistency at zero or the lack of inverse integral operator. On the other hand, we build a novel…
The aim of this paper is to study differential and spectral properties of the infinitesimal operator of two dimensional Markov processes with diffusion and discrete components. The infinitesimal operator is now a second-order differential…
Signal scaling is a fundamental operation of practical importance in which a signal is enlarged or shrunk in the coordinate direction(s). Scaling or magnification is not trivial for signals of a discrete variable since the signal values may…
We propose an approximation of nonlinear renewal equations by means of ordinary differential equations. We consider the integrated state, which is absolutely continuous and satisfies a delay differential equation. By applying the…
We introduce two kinds of fractional integral operators; the one is defined via the exponential-integral function $$ E_1(x)=\int_x^\infty \frac{e^{-t}}{t}\,dt,\quad x>0, $$ and the other is defined via the special function $$…
In this paper we focus on the linear functionals defining an approximate version of the gradient of a function. These functionals are often used when dealing with optimization problems where the computation of the gradient of the objective…
It is known that the unified transform method may be used to solve any well-posed initial-boundary value problem for a linear constant-coefficient evolution equation on the finite interval or the half-line. In contrast, classical methods…
Computing many eigenpairs of the Schr{\"o}dinger operator presents a computational bottleneck in large-scale quantum simulations due to the global communication overhead of explicit orthogonalization. To address this issue, we propose a…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
We present a novel attention-based model for discrete event data to capture complex non-linear temporal dependence structures. We borrow the idea from the attention mechanism and incorporate it into the point processes' conditional…
This work is devoted to the obtaining of a new numerical scheme based in quadrature formulas for the Lebesgue-Stieltjes integral for the approximation of Stieltjes ordinary differential equations. This novel method allows us to numerically…