This thesis discusses strategies for numerically solving a two dimensional integral. The difficulties here are due to numerous integrands and regions in R2. The transformation to units as the 2-simplex and the cube can simplify many integrands. An approach to arbitrary regions is to decompose them into easy ones as triangles and rectangles. For these regions formulas that approximate the two di...

We study the kernels of the remainder term Rn,s(f) of GaussTurán quadrature formulas ∫ 1 −1 f(t)w(t) dt = n ∑

We show that, for a finite set A of real numbers, the size of the set A + A A + A = { a + b c + d : a, b, c, d ∈ A, c + d 6= 0 } is bounded from below by ∣∣∣∣A + A A + A ∣∣∣∣ |A|2+1/4 |A/A|1/8 log |A| . This improves a result of Roche-Newton (2016).

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...

In this work, a new family of time marching procedures based on Green’s function matrices is presented. The formulation is based on the development of new recurrence relationships, which employ time integral terms to treat initial condition values. These integral terms are numerically evaluated taking into account Newton-Cotes formulas. The Green’s matrices of the model are also numerically com...

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...