Spectral methods yield numerical solutions of the Galerkin-truncated versions of nonlinear
partial differential equations (PDEs) involved especially in fluid dynamics. In the presence of …

In this paper, we study a novel numerical scheme for the fourth order partial integro-
differential equation with a weakly singular kernel. In the time direction, a Crank–Nicolson …

We propose a modification of the sampling series using a Gaussian multiplier. Error
estimates for the modified series to approximate a band-limited function and its derivatives …

An optimal algorithm for approximating bandlimited functions from localized sampling is
established. Several equivalent formulations for the approximation error of the optimal …

In this paper, we discuss some numerical realizations of Shannon's sampling theorem. First
we show the poor convergence of classical Shannon sampling sums by presenting sharp …

In this article, we consider the reconstruction of a bandlimited function from its finite localized
sample data. Truncating the classical Shannon sampling series results in an unsatisfactory …

In this paper, we present new regularized Shannon sampling formulas which use localized
sampling with special window functions, namely Gaussian, B-spline, and sinh-type window …

Graph Neural Network (GNN) with its ability to integrate graph information has been widely
used for data analyses. However, the expressive power of GNN has only been studied for …

The reconstruction of a bandlimited function from its finite sample data is fundamental in
signal analysis. It is well known that oversampling of a bandlimited function leads to …

The fast reconstruction of a bandlimited function from its sample data is an essential problem
in signal processing. In this paper, we consider the widely used Gaussian regularized …