Weighted quadrature rules with binomial nodes

Explicit forms of weighted quadrature rules with geometric nodes

a f (x)w(x) dx = n − k=0 wkf (xk) + Rn+1[f ], where w(x) is a weight function, {xk}k=0 are integration nodes, {wk} n k=0 are the corresponding weight coefficients, and Rn+1[f ] denotes the error term. During the past decades, various kinds of formulae of the above type have been developed. In this paper, we introduce a type of interpolatory quadrature, whose nodes are geometrically distributed ...

Quadrature rules with multiple nodes

In this paper a brief historical survey of the development of quadrature rules with multiple nodes and the maximal algebraic degree of exactness is given. The natural generalization of such rules are quadrature rules with multiple nodes and the maximal degree of exactness in some functional spaces that are different from the space of algebraic polynomial. For that purpose we present a generaliz...

Weighted Quadrature Rules for Finite Element Methods

We discuss the numerical integration of polynomials times exponential weighting functions arising from multiscale finite element computations. The new rules are more accurate than standard quadratures and are better suited to existing codes than formulas computed by symbolic integration. We test our approach in a multiscale finite element method for the 2D reaction-diffusion equation. Standard ...

Quadrature With Respect to Binomial Measures

This work is devoted to the study of integration with respect to binomial measures. We develop interpolation quadrature rules and study their properties. Applying a local error estimate based on null rules, we test two automatic integrators with local quadrature rules that generalize the five points Newton Cotes formula.

Quadrature Rules for Fuzzy Integrals

A New Approach to the Quadrature Rules with Gaussian Weights and Nodes

To compute integrals on bounded or unbounded intervals we propose a new numerical approach by using weights and nodes of the classical Gauss quadrature rules. An account of the error and the convergence theory is given for the proposed quadrature formulas which have the advantage of reducing the condition number of the linear system arising when applying Nyström methods to solve integral equati...