By a recent result on subperiodic trigonometric Gaussian quadrature, we construct a cubature formula of algebraic degree of exactness n on planar circular lenses (intersection of two overlapping disks) and “double bubbles” (union of two overlapping disks), with n2/2+O(n) nodes. An application is shown to RBF projection methods. 2000 AMS subject classification: 65D32.

We study a new simple quadrature rule based on integrating a C1 quadratic spline quasi-interpolant on a bounded interval. We give nodes and weights for uniform and non-uniform partitions. We also give error estimates for smooth functions and we compare this formula with Simpson’s rule.

A numerical method to solve Abel-type integral equations of first kind is given. In this paper we suggest the research of a numerical solution for Abel-type integral equations of the first kind, by using a collocation method employing an interpolatory product-quadrature formula with a trigonometric polynomial of the first order. Some results of numerical examples are reported.

A gaussian type quadrature formula, where the nodes are the zeros of Bessel functions of the first kind of order α (<(α) > −1), was recently proved for entire functions of exponential type. Here we relax the restriction on α as well as on the function. Some applications are also given.

This article considers the error of integrating multivariate Haar wavelet series by quasi-Monte Carlo rules using scrambled digital nets. Both the worst-case and random-case errors are analyzed. It is shown that scrambled net quadrature has optimal order. Moreover, there is a simple formula for the worst-case error.

We show how to combine incidence matrices, which admit Hermite-Birkhoff quadrature formulas of Gaussian type for any positive measure, in such a way that the resulting matrix also admits Gaussian type quadratures for any positive measure. Moreover, the uniqueness property and the extremal property of the formulas corresponding to the submatrices are transferred to the formula admitted by the co...

A fifth degree approximate integration formula for hypercubes is constructed. If the integrand is a real function of n independent real variables and the integer number k satisfying the condition 1 ≤ k < n is given, then a 2 + (n k ) 2 + 1 point non–product quadrature is obtained. In the case n = 4, some comparative numerical examples are considered.

After some remarks on the convergence order of the classical gaussian formula for the numerical evaluation of integrals on unbounded interval, the authors develop a new quadrature rule for the approximation of such integrals of interest in the practical applications. The convergence of the proposed algorithm is considered and some numerical examples are given.

We prove that to every rational function R(z) satisfying R(−z)R(z) = 1, there exists a symplectic Runge-Kutta method with R(z) as stability function. Moreover, we give a surprising relation between the poles of R(z) and the weights of the quadrature formula associated with a symplectic Runge-Kutta method.

Numerical approximations of definite integrals and related error estimations can be made using Simpson’s rules (inequalities). There are two well-known rules: 13 rule or quadrature formula 38 second formula. The aim the present paper is to extend several inequalities that hold for rule. More precisely, we prove a weighted version type inequality some Lipschitzian, bounded variations, convex fun...