Related papers: Oscillatory behaviour of the RBF-FD approximation …
For fiber-fed spectrographs with a stable external wavelength source, scrambling properties of optical fibers and, homogeneity and stability of the instrument illumination are important for the accuracy of radial-velocimetry. Optical…
Quantifying the effects on electromagnetic waves scattered by objects of uncertain shape is key for robust design, particularly in high precision applications. Assuming small random perturbations departing from a nominal domain, the…
Classical probabilistic rounding error analysis is particularly well suited to stochastic rounding (SR), and it yields strong results when dealing with floating-point algorithms that rely heavily on summation. For many numerical linear…
While pseudospectral (PS) methods can feature very high accuracy, they tend to be severely limited in terms of geometric flexibility. Application of global radial basis functions overcomes this, however at the expense of problematic…
The next generation of space-based telescopes used for weak lensing surveys will require exquisite point spread function (PSF) determination. Previously negligible effects may become important in the reconstruction of the PSF, in part…
With recent advances in scanning probe microscopy (SPM), it is now routine to determine the atomic structure of surfaces and molecules while quantifying the local tip-sample interaction potentials. Such quantitative experiments are based on…
We present a novel hyperviscosity formulation for stabilizing RBF-FD discretizations of the advection-diffusion equation. The amount of hyperviscosity is determined quasi-analytically for commonly-used explicit, implicit, and…
We discuss the origin of the finite size error of the energy in many-body simulation of systems of charged particles and we propose a correction based on the random phase approximation at long wave lengths. The correction comes from…
This paper considers the numerical analysis of a semilinear fractional diffusion equation with nonsmooth initial data. A new Gr\"onwall's inequality and its discrete version are proposed. By the two inequalities, error estimates in three…
In this paper we obtain approximated numerical solutions for the 2D Helmholtz equation using a radial basis function-generated finite difference scheme (RBF-FD), where weights are calculated by applying an oscillatory radial basis function…
In this work, we implement a relatively new analytical technique, the Improved Amplitude-Frequency Formulation (IAFF) method, approach for solving accurate approximate analytical solutions for strong nonlinear oscillators, which may contain…
This paper investigates the role of the augmentation parameter in the Finite Selection Model (FSM) and its impact on estimator performance. Through a comprehensive Monte Carlo simulation study, we analyze the sensitivity of bias, variance,…
We study asymptotic error distributions associated with standard approximation scheme for one-dimensional stochastic differential equations driven by fractional Brownian motions. This problem was studied by, for instance, Gradinaru-Nourdin…
The paper introduces a new meshfree pseudospectral method based on Gaussian radial basis functions (RBFs) collocation to solve fractional Poisson equations. Hypergeometric functions are used to represent the fractional Laplacian of Gaussian…
Computable Stein discrepancies have been deployed for a variety of applications, ranging from sampler selection in posterior inference to approximate Bayesian inference to goodness-of-fit testing. Existing convergence-determining Stein…
We investigate the spectrum of differentiation matrices for certain operators on the sphere that are generated from collocation at a set of scattered points $X$ with positive definite and conditionally positive definite kernels. We focus on…
Scaling relationships, both integrated and spatially resolved, arise due to the physical processes that govern galaxy evolution and are frequently measured in both observed and simulated data. However, the accuracy and comparability of…
Numerical multiscale methods usually rely on some coupling between a macroscopic and a microscopic model. The macroscopic model is incomplete as effective quantities, such as the homogenized material coefficients or fluxes, are missing in…
This article deals with stochastic partial differential equations with quadratic nonlinearities perturbed by small additive and multiplicative noise. We present the approximate solution of the original equation via the amplitude equation…
Meshing of geometric domains having curved boundaries by affine simplices produces a polytopial approximation of those domains. The resulting error in the representation of the domain limits the accuracy of finite element methods based on…