In recent years a number of authors have considered an error analysis for quadrature rules of Newton-Cotes type. In particular, the mid-point, trapezoid and Simpson rules have been investigated more recently ([2], [4], [5], [6], [11]) with the view of obtaining bounds on the quadrature rule in terms of a variety of norms involving, at most, the first derivative. In the mentioned papers explicit...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 4 January 2021Accepted: 07 June 2021Published online: 03 February 2022KeywordsGauss quadrature, Gauss--Hermite, Newton--Cotes, Clenshaw--Curtis, cubatureAMS Subject Headings41A55, 65D32Publication DataISSN (print): 0036-1445ISSN (online): 1095-7200Publisher: Society for I...

In this paper, a numerical method for integration of fuzzy functions is considered. Fuzzy Newton-Cotes formula, such as fuzzy trapezoidal method and fuzzy Simpson method are calculated by integration of fuzzy functions on two and three equally space points. Also the composite fuzzy trapezoidal and composite fuzzy Simpson method are proposed for n equally space points. The proposed method are il...

hybrid of rationalized haar functions are developed to approximate the solution of the differential equations. the properties of hybrid functions which are the combinations of block-pulse functions and rationalized haar functions are first presented. these properties together with the newton-cotes nodes are then utilized to reduce the differential equations to the solution of algebraic equation...

The collocation method based on cubic B-spline, is developed to approximate the solution of second kind nonlinear Fredholm integral equations. First of all, we collocate the solution by B-spline collocation method then the Newton-Cotes formula use to approximate the integrand. Convergence analysis has been investigated and proved that the quadrature rule is third order convergent. The presented...