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View article: Approximation of the Hilbert Transform On The Unit Circle
Approximation of the Hilbert Transform On The Unit Circle Open
The paper deals with the numerical approximation of the Hilbert transform on the unit circle using Szegő and anti-Szegő quadrature formulas. These schemes exhibit maximum precision with oppositely signed errors and allow for improved accur…
View article: Approximation of the Hilbert Transform on the unit circle
Approximation of the Hilbert Transform on the unit circle Open
The paper deals with the numerical approximation of the Hilbert transform on the unit circle using Szegö and anti-Szegö quadrature formulas. These schemes exhibit maximum precision with oppositely signed errors and allow for improved accur…
View article: A global approximation method for second-kind nonlinear integral equations
A global approximation method for second-kind nonlinear integral equations Open
A global approximation method of Nyström type is explored for the numerical solution of a class of nonlinear integral equations of the second kind. The cases of smooth and weakly singular kernels are both considered. In the first occurrenc…
View article: Averaged Nyström interpolants for bivariate Fredholm integral equations on the real positive semi-axes
Averaged Nyström interpolants for bivariate Fredholm integral equations on the real positive semi-axes Open
Nyström interpolants based on suitable anti-Gauss cubature formulae associated with the Laguerre weights are provided for the numerical solution of second-kind Fredholm integral equations defined on the first quadrant in the coordinate pla…
View article: Averaged Nyström interpolants for the solution of Fredholm integral equations of the second kind
Averaged Nyström interpolants for the solution of Fredholm integral equations of the second kind Open
Fredholm integral equations of the second kind that are defined on a finite or infinite interval arise in many applications. This paper discusses Nyström methods based on Gauss quadrature rules for the solution of such integral equations. …
View article: Anti-Gauss cubature rules with applications to Fredholm integral equations on the square
Anti-Gauss cubature rules with applications to Fredholm integral equations on the square Open
The purpose of this paper is to develop the anti-Gauss cubature rule for approximating integrals defined on the square whose integrand function may have algebraic singularities at the boundaries. An application of such a rule to the numeri…
View article: On the error of best polynomial approximation of composite functions
On the error of best polynomial approximation of composite functions Open
The purpose of the paper is to provide a characterization of the error of the best polynomial approximation of composite functions in weighted spaces. Such a characterization is essential for the convergence analysis of numerical methods a…
View article: Averaged Nyström interpolants for the solution of Fredholm integral equations of the second kind
Averaged Nyström interpolants for the solution of Fredholm integral equations of the second kind Open
Fredholm integral equations of the second kind that are defined on a finite or infinite interval arise in many applications. This paper discusses Nyström methods based on Gauss quadrature rules for the solution of such integral equations. …
View article: On the numerical solution of Volterra integral equations on equispaced nodes
On the numerical solution of Volterra integral equations on equispaced nodes Open
In the present paper, a Nystrom-type method for second kind Volterra integral equations is introduced and studied. The method makes use of generalized Bernstein polynomials, defined for continuous functions and based on equally spaced poin…
View article: A PROJECTION METHOD FOR VOLTERRA INTEGRAL EQUATIONS IN WEIGHTED SPACES OF CONTINUOUS FUNCTIONS
A PROJECTION METHOD FOR VOLTERRA INTEGRAL EQUATIONS IN WEIGHTED SPACES OF CONTINUOUS FUNCTIONS Open
This paper is concerned with the numerical treatment of second kind Volterra integral equations whose integrands present diagonal and/or endpoint algebraic singularities. A projection method based on an optimal interpolating operator is de…
View article: A product integration rule on equispaced nodes for highly oscillating integrals
A product integration rule on equispaced nodes for highly oscillating integrals Open
This paper provides a product integration rule for highly oscillating integrands, based on equally spaced nodes. The stability and the error estimate are proven in the space of continuous functions, and some numerical tests which confirm s…
View article: On the numerical solution of Volterra integral equations on equispaced nodes
On the numerical solution of Volterra integral equations on equispaced nodes Open
In the present paper, a Nystrom-type method for second kind Volterra integral equations is introduced and studied. The method makes use of generalized Bernstein polynomials, defined for continuous functions and based on equally spaced poin…
View article: Volterra integral equations with highly oscillatory kernels: a new numerical method with applications
Volterra integral equations with highly oscillatory kernels: a new numerical method with applications Open
The aim of this paper is to present a Nyström-type method for the numerical approximation of the solution of Volterra integral equations of the second kind having highly oscillatory kernels. The method is based on a mixed quadrature scheme…
View article: A numerical method for the generalized Love integral equation in 2D
A numerical method for the generalized Love integral equation in 2D Open
This paper deals with the numerical solution of the generalized Love integral equation defined on the square. The method is of Nyström type and is based on the approximation of the integral by a product cubature rule whose coefficients are…
View article: Numerical treatment of the generalized Love integral equation
Numerical treatment of the generalized Love integral equation Open
In this paper, the generalized Love integral equation has been considered. In order to approximate the solution, a Nyström method based on a mixed quadrature rule has been proposed. Such a rule is a combination of a product and a “dilation…
View article: Vehicular traffic, crowds, and swarms: From kinetic theory and multiscale methods to applications and research perspectives
Vehicular traffic, crowds, and swarms: From kinetic theory and multiscale methods to applications and research perspectives Open
This paper presents a review and critical analysis on the modeling of the dynamics of vehicular traffic, human crowds and swarms seen as living and, hence, complex systems. It contains a survey of the kinetic models developed in the last 1…
View article: Scattering data computation for the Zakharov-Shabat system
Scattering data computation for the Zakharov-Shabat system Open
A numerical method to solve the direct scattering problem for the Zakharov-Shabat system associated to the initial value problem for the nonlinear Schroedinger equation is proposed. The method involves the numerical solution of Volterra in…