The collocation methods based on cubic B-spline, are developed to approximate solution of the second and first kind Fredholm integral equations.First we collocate the solution by B-spline and the Newton-Cotes formula is used to approximate integral. Convergence analysis has been investigated and proved that the quadratur rule is fourth order convergent. The presented methods are tested to the p...

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...

A collocation procedure is developed for the linear and nonlinear Fredholm and Volterraintegro-differential equations, using the globally defined B-spline and auxiliary basis functions.The solutionis collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula.The error analysis of proposed numerical method is studied theoretically. Numerical results are given toil...

In this paper, we found the error bounds for one of open Newton–Cotes formulas, namely Milne’s formula differentiable convex functions in framework fractional and classical calculus. We also give some mathematical examples to show that newly established are valid formula.

Interactions are explored through the observation of the dynamics of particles. On the classical level the basic underlying assumption in that scheme is that Newton's second law holds. Relaxing the validity of this axiom by, e.g., allowing for higher order time derivatives in the equations of motion would allow for a more general structure of interactions. We derive the structure of interaction...

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.

the spline collocation method  is employed to solve a system of linear and nonlinear fredholm and volterra integro-differential equations. the solutions are collocated by cubic b-spline and the integrand is approximated by the newton-cotes formula. we obtain the unique solution for linear and nonlinear system $(nn+3n)times(nn+3n)$ of integro-differential equations. this approximation reduces th...

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...

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...