Chebfun is an established software system for computing with functions of a real variable, but its capabilities for handling functions with singularities are limited. Here an analogous system is described based on sinc function expansions instead of Chebyshev series. This experiment sheds light on the strengths and weaknesses of sinc function techniques. It also serves as a review of some of th...

This article is a response to E. Heit and B. K. Hayes’s (2005) comment on the target article “Induction and Categorization in Young Children: A Similarity-Based Model” (V. M. Sloutsky & A. V. Fisher, 2004a). The response discusses points of agreement and disagreement with Heit and Hayes; phenomena predicted by similarity, induction, naming, and categorization (SINC); and relationships between S...

We investigate the behavior of imperfect band-limited occulting masks in a high-contrast imaging system through modeling and simulations. Grayscale masks having 1D Sinc(2) (linear-Sinc(2)) amplitude transmission coefficient (Sinc(4) intensity transmittance) profiles as well as optical density and wavelength-dependent parasitic phases are considered occulters. We compare the behaviors of several...

We consider the application of a Sinc-Collocation approach based on first derivative to solve boundary value problems (BVPs) arising from fluid dynamics related models. Even in the presence of singularities that are often present in fluid dynamics problems involving boundary layers, the Sinccollocation technique provides exponentially convergent approximations including those posed on unbounded...

In this work, we study the performance of the sinc-Collocation method for solving Bratu's problem. For different choices of step size, we consider the maximum absolute errors in the solutions at sinc grid points and tabulated in tables. The comparison of the obtained results veri ed that this method converges to the exact solution rapidly and with  

Sinc methods are now recognized as an efficient numerical method for problems whose solutions may have singularities, or infinite domains, or boundary layers. This work deals with the sinc-collocation method for solving linear and nonlinear system of second order differential equation. The method is then tested on linear and nonlinear examples and a comparison with B-spline method is made. It i...

In this paper, Solvability nonlinear Volterra integral equations with general vanishing delays is stated. So far sinc methods for approximating the solutions of Volterra integral equations have received considerable attention mainly due to their high accuracy. These approximations converge rapidly to the exact solutions as number sinc points increases. Here the numerical solution of nonlinear d...

Abstract The purpose of this paper is the evaluation Fourier transform powers sinc function multiplied by monomials, also in cases when log terms arise. Such evaluations appear only rarely literature. Some old sources are hardly available. Because notations not use today, several original works difficult to read. We apply an approach J. H. Michell a variant G. Hardy integrals over and their tra...

The problem of digital signal and image resampling with discrete sinc interpolation is addressed. Discrete sine interpolation is theoretically the best one among the digital convolution-based signal resampling methods because it does not distort the signal as defined by its samples and is completely reversible. However, sinc interpolation is frequently not considered in applications because it ...

This paper presents meshfree method for solving systems of linear Volterra integro-differential equations with initial conditions. This approach is based on collocation method using Sinc basis functions. It's well-known that the Sinc approximate solution converges exponentially to the exact solution. Some numerical results are included to show the validity of this method.