Sinc Function Quadrature Rules for the Fourier Integral

Sine Function Quadrature Rules for the Fourier Integral

In this paper a numerical algorithm is proposed for the computation of the Fourier Transform. The quadrature rule developed is based on the Whittaker Cardinal Function expansion of the integrand and a certain Conformai Map. The error of the method is analyzed and numerical results are reported which confirm the accuracy of the quadrature rule.

A Sinc Quadrature Method for the Urysohn Integral Equation

In this paper, we study the numerical approximation of the Urysohn integral equation with two methods. The methods are developed by means of the sinc approximation with the Single Exponential (SE) and Double Exponential (DE) transformations. These numerical methods combine a sinc Nyström method with the Newton iterative process that involves solving a nonlinear system of equations. We provide a...

Quadrature Rules for Fuzzy Integrals

Efficient quadrature rules for a class of cordial Volterra integral equations: A comparative study

‎A natural algorithm with an optimal order of convergence is proposed for numerical solution of a class of cordial weakly singular Volterra integral equations‎. ‎The equations of this class appear in heat conduction problems with mixed boundary conditions‎. ‎The algorithm is based on a representation of the solution and compound Gaussian quadrature rules with graded meshes‎. ‎A comparative stud...

Relative Convexity and Quadrature Rules for the Riemann–stieltjes Integral

We develop Trapezoid, Midpoint, and Simpson’s rules for the Riemann-Stieltjes integral, the latter two being new. These rules are completely natural when the notion of relative convexity is used. Mathematics subject classification (2010): 65D30.