In this paper, we generalize Cerone’s results, and a unified treatment of error estimates for a general inequality satisfying f (n−1) being of bounded variation is presented. We derive the estimates for the remainder terms of the mid-point, trapezoid, and Simpson formulas. All constants of the errors are sharp. Applications in numerical integration are also given. c © 2007 Elsevier Ltd. All rig...

in this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. we utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. by using bernstein polynomial basis, the problem is transformed in...

the purpose of this study is to implement a new modification of the variational iteration method (h-s-vim), which is a combination of spectral method and variational iteration method for heat transfer problems with high nonlinearity order. the merit of this method is that it does not require the solution of any linear or nonlinear system of equations unlike spectral method. furthermore the prop...

Abstract Numerous product quality scandals are caused by low-quality inputs. When input is not perfectly observed downstream firms, upstream firms often have moral hazard problems. If vertical integration does directly eliminate the problems, still improve quality? so, under which conditions? We find that given precision of monitoring technology used when level public very high or low, no incen...

User expectations regarding new products and services are evolving rapidly, forcing innovative organizations to explore avenues for innovation, combining services. This paper focuses on the integrative design of product–service systems (PSSs) builds servitization service-based innovation literature. Many tools have been proposed designing integrated PSS, with intent generate economic and/or sus...