In this paper, a numerical solution for a system of linear Fredholm integro-differential equations by means of the sinc method is considered. This approximation reduces the system of integro-differential equations to an explicit system of algebraic equations. The exponential convergence rate $O(e^{-k sqrt{N}})$ of the method is proved. The analytical results are illustrated with numerical examp...

the aim of this paper is to present a new numerical method for solving the bagley-torvik equation. this equation has an important role in fractional calculus. the fractional derivatives are described based on the caputo sense. some properties of the sinc functions required for our subsequentdevelopment are given and are utilized to reduce the computation of solution of the bagley-torvik equatio...

in this study, the bernoulli polynomials are used to obtain an approximate solution of a class of nonlinear two-dimensional integral equations. to this aim, the operational matrices of integration and the product for bernoulli polynomials are derived and utilized to reduce the considered problem to a system of nonlinear algebraic equations. some examples are presented to illustrate the efficien...

We present a translation of sequential ASMs to Event-B specifications. The translation also addresses the partial update problem, and allows a variable to be updated (consistently) in parallel. On the theoretical side, the translation highlights the intricacies of ASM rule execution in terms of Event-B semantics. On the practical side, we show on a series of examples that the Event-B encoding r...

nowadays, advances in information and communication technologies, has provided an opportunity for banks to provide their electronic services to their customers in remote areas. this technological innovation by e–banking systems has brought about many benefits to customers while it has been accompanied by a number of risks including the operational ones. this risks need to be identified and mana...

In this paper, we present a new computational method to solve Volterra integral equations of the first kind based on Bernstein polynomials. In this method, using operational matrices turn the integral equation into a system of equations. The computed operational matrices are exact and new. The comparisons show this method is acceptable. Moreover, the stability of the proposed method is studied.

In the paper a relatively simple yet powerful and versatile technique for forecasting time series data – simple exponential smoothing is described. The simple exponential smoothing (SES) is a short-range forecasting method that assumes a reasonably stable mean in the data with no trend (consistent growth or decline). It is one of the most popular forecasting methods that uses weighted moving av...