Many numerical methods have been developed for the solution of Poisson and Laplace equations such as finite-difference methods, finite-element methods, boundary-element methods, etc. Sinc numerical methods developed recently by Stenger and co-workers excel over other methods for problems involving singularities, infinite or semi-infinite domains as well as boundary layer behaviors. In this pape...

A Gaussian-Sinc basis set methodology is presented for the calculation of the electronic structure of atoms and molecules at the Hartree-Fock level of theory. This methodology has several advantages over previous methods. The all-electron electronic structure in a Gaussian-Sinc mixed basis spans both the "localized" and "delocalized" regions. A basis set for each region is combined to make a ne...

sinc-galerkin method based upon double exponential transformation for solving troesch's problem was given in this study. properties of the sinc-galerkin approach were utilized to reduce the solution of nonlinear two-point boundary value problem to same nonlinear algebraic equations, also, the matrix form of the nonlinear algebraic equations was obtained.the error bound of the method was fo...

We test the Sinc function representation, a novel method for numerically evaluating Feynman diagrams, by using it to evaluate the three-loop master diagrams. Analytical results have been obtained for all these diagrams, and we find excellent agreement between our calculations and the exact values. The Sinc function representation converges rapidly, and it is straightforward to obtain accuracies...

We extend our new approach for numeric evaluation of Feynman diagrams to integrals that include fermionic and vector propagators. In this initial discussion we begin by deriving the Sinc function representation for the propagators of spin1 2 and spin-1 fields and exploring their properties. We show that the attributes of the spin-0 propagator which allowed us to derive the Sinc function represe...

The present study investigates the Haar-Sinc collocation method for the solution of the hyperbolic partial telegraph equations. The advantages of this technique are that not only is the convergence rate of Sinc approximation exponential but the computational speed also is high due to the use of the Haar operational matrices. This technique is used to convert the problem to the solution of linea...

Sinc-collocation scheme is one of the new techniques used in solving numerical problems involving integral equations. This method has been shown to be a powerful numerical tool for finding fast and accurate solutions. So, in this paper, some properties of the Sinc-collocation method required for our subsequent development are given and are utilized to reduce integral equation of the first kind ...

We show that a variety of trigonometric sums have unexpected closed forms by relating them to cognate integrals. 1 Motivation Recall that sinc(x) := sin(x)/x when x 6= 0 and sinc(0) := 1. In [4] and [8], it was shown that, for N = 0, 1, 2, 3, 4, 5, and 6, ∫ ∞

There are few techniques available to numerically solve contaminant transport equation. In this paper we show that the Sinc-Galerkin method is a very effective tool in numerically solving contaminant transport equation. The numerical results demonstrate the reliability and efficiency of using the Sinc-Galerkin method to solve such problems.

A collocation procedure is developed for the linear and nonlinear Volterra integral equations, using the globally defined Sinc and auxiliary basis functions. We analytically show the exponential convergence of the Sinc collocation method for approximate solution of Volterra integral equations. Numerical examples are included to confirm applicability and justify rapid convergence of our method.