On weighted three point quadrature rules

Weighted quadrature rules with binomial nodes

In this paper, a new class of a weighted quadrature rule is represented as --------------------------------------------  where  is a weight function,  are interpolation nodes,  are the corresponding weight coefficients and denotes the error term. The general form of interpolation nodes are considered as   that  and we obtain the explicit expressions of the coefficients  using the q-...

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 Rules for Fuzzy Integrals

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 on unbounded interval

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.