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.

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.

We present improved algorithms for fast calculation of the inverse square root for single-precision floating-point numbers. The algorithms are much more accurate than the famous fast inverse square root algorithm and have the same or similar computational cost. The main idea of our work consists in modifying the NewtonRaphson method and demanding that the maximal error is as small as possible. ...

In this paper, we consider the finite element method for time fractional partial differential equations. The existence and uniqueness of the solutions are proved by using the Lax-Milgram Lemma. A time stepping method is introduced based on a quadrature formula approach. The fully discrete scheme is considered by using a finite element method and optimal convergence error estimates are obtained....

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...

In the present work we have studied superconvergence of Hadamard finite-part integral. We have studied the second-order and the third-order quadrature formulae of Newton-Cotes type. We follow works [Sun, Wu, 2005b], [Lü, Wu, 2005] and work [Wu, Yu and Zhang, 2009] and introduce new rule which gives the same convergence rate as rules in [Lü and Wu, 2005] and [Wu, Yu and Zhang, 2009] but in more ...

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...

J. E. COTES Breathlessness is one of a number of symptoms which may limit exercise; it usually does so when the ventilation during exercise approaches a maximal value which is determined by interaction between the drive to respiration and the mechanical properties of the lung. Assessment is based in the first instance on the clinical interview and simple measurements of lung function. Depending...