we reduce the two phase stefan problem with kinetic to a system of nonlinear volterra integral equations of second kind and apply newton's method to linearize it. we found product integration solution of the linear form. sufficient conditions for convergence of the numerical method are given and their applicability is illustrated with an example.

we develop and apply the product integration method to a large class of linear weakly singular volterra systems. we show that under certain sufficient conditions this method converges. numerical implementation of the method is illustrated by a benchmark problem originated from heat conduction.

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 computational method based on using the operational matrix of anorthogonal function for solving variational problems is computeroriented. In this approach, a truncated Hartley series together withthe operational matrix of integration and integration of the crossproduct of two cas vectors are used for finding the solution ofvariational problems. Two illustrative...

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...