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, ∫ ∞

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.

‎In this paper‎, ‎the numerical solutions of linear and nonlinear Volterra integral‎ ‎equations with nonvanishing delay are considered by two methods‎. ‎The methods are developed by means of‎ ‎the sinc approximation with the single exponential (SE) and double exponential (DE)‎ ‎transformations‎. ‎The existence and uniqueness of sinc-collocation solutions for these equations are provided‎. ‎Thes...

Tensor-product approximation provides a convenient tool for efficient numerical treatment of high dimensional problems that arise, in particular, in electronic structure calculations in Rd. In this work we apply tensor approximation to the Galerkin representation of the Newton and Yukawa potentials for a set of tensor-product, piecewise polynomial basis functions. To construct tensor-structured...

In Medical Image Computing and Computer-Assisted Intervention – MICCAI 1999, C. Taylor and A. Colchester (eds.), vol. 1679 of Lecture Notes in Computer Science, Springer-Verlag, Berlin, 1999, pp. 210–217. Abstract. Interpolation is required in many medical image processing operations. From sampling theory, it follows that the ideal interpolation kernel is the sinc function, which is of infinite...

We present a numerical method for approximating an indefinite integral by the double exponential sinc method. The approximation error of the proposed method with N integrand function evaluations is O(exp(−c1N/ log(c2N))) for a reasonably wide class of integrands, including those with endpoint singularities. The proposed method compares favorably with the existing formulas based on the ordinary ...

In this paper, a numerical procedure for solving a class of nonlinear VolterraFredholm integral equations is presented. The method is based upon the globally defined sinc basis functions. Properties of the sinc procedure are utilized to reduce the computation of the nonlinear integral equations to some algebraic equations. Illustrative examples are included to demonstrate the validity and appli...

Tthis paper, is concerned with obtaining numerical solutions for a class of convection-diffusion equations (CDEs) with variable coefficients. Our approaches are based on collocation methods. These approaches implementing all four kinds of shifted Chebyshev polynomials in combination with Sinc functions to introduce an approximate solution for CDEs . This approximate solution can be expressed as...