In this paper, using a new identity, we study one of the famous Newton-Cotes three-point quadraturerules. More precisely Maclaurin’s quadrature rule, for which establish error estimate methodunder constraint that first derivatives belong to class preinvex functions. We also give someapplications special means as applications. believe studied inequality and resultsobtained in article will furthe...

We show how ideas originating in the theory of dynamical systems inspire a new approach to numerical integration of functions. Any Lebesgue integral can be approximated by a sequence of integrals with respect to equidistributions, i.e. evenly weighted discrete probability measures concentrated on an equidistributed set. We prove that, in the case where the integrand is real analytic, suitable l...

The main objective of the study is to compare the Newton-Cotes methods such as the Trapezium rule, Simpson 1/3 rule and Simpson 3/8 rule to estimate the area under the Lorenz curve and Gini coefficient of income using polynomial function with degree 5. Comparing the Gini coefficients of income computed from the Polynomial function with degree 5 for the Trapezium, Simpson 1/3 and Simpson 3/8 met...

in this paper, we use parametric form of fuzzy number, then aniterative approach for obtaining approximate solution for a classof nonlinear fuzzy fredholmintegro-differential equation of the second kindis proposed. this paper presents a method based on newton-cotesmethods with positive coefficient. then we obtain approximatesolution of the nonlinear fuzzy integro-differential equations by an it...

2. Write a Matlab script of no more than 10 lines to calculate the Newton-Cotes quadrature weights wj , j = 1, 2, . . . , n, n + 1; go to the end of this handout for more details about wj . For uniformity, we require that the script starts with the four lines n=2; h=1/n; nodes=(0:h:1)’; f=eye(n+1); where the j-th column of the matrix f are needed for the Lagrange interpolation in order to find ...

The exact order of deterministic, stochastic and average error bounds of multidimensional quadrature formulas for anisotropic Sobolev class W r pðIÞ; Nikolskii class H pðIÞ and their periodic analogue is obtained. It is proved that if p41; then the stochastic and average error bounds are essentially smaller than the deterministic error bounds. Nonlinear methods, adaptive methods, or even method...

In earlier work we have studied a method for discretization in time of a parabolic problem, which consists of representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In application to a spatially semidiscrete finite-element version of the parabolic problem, at each quadrature point one then needs to solve a linear algebraic sy...