مجله بین المللی محاسبات و مدل سازی ریاضی
سال هفتم شماره 4 (Autumn 2017)

This paper presents the analysis of a continuous review perishable inventory system wherein the life time of each item follows an exponential distribution. The operating policy is (s,S) policy where the ordered items are received after a random time which follows exponential distribution. Primary arrival follows Poisson distribution and they may turnout to be positive or negative and then enter into the orbit. The orbiting demands compete their service according to exponential distribution. The server takes multiple working vacations at zero inventory. We assume that the vacation time, service times both during regular busy period and vacation period are exponentially distributed. Matrix analytic method is used for the steady state distribution of the model. Various performance measures and cost analysis are shown with numerical results.

A simple method for solving Prandtl's integro-differential equation is proposed based on a new reproducing kernel space. Using a transformation and modifying the traditional reproducing kernel method, the singular term is removed and the analytical representation of the exact solution is obtained in the form of series in the new reproducing kernel space. Compared with known investigations, its advantages are that the representation of the exact solution is obtained in a reproducing kernel Hilbert space and accuracy in numerical computation is higher. On the other hand, the approximate solution and its derivatives converge uniformly to the exact solution and its derivatives. The final numerical experiments illustrate the method is efficient.

This paper presents a computational technique that called Tau-collocation method for the developed solution of non-linear integro-differential equations which involves a population model. To do this, the nonlinear integro-differential equations are transformed into a system of linear algebraic equations in matrix form without interpolation of non-poly-nomial terms of equations. Then, using collocation points, we solve this system and obtain the unknown coefficients. To illustrate the ability and reliability of the method some nonlinear integro-differential equations and population models are presented. The results reveal that the method is very effective and simple.

‎Radial basis function method has been used to handle linear and‎ ‎nonlinear equations‎. ‎The purpose of this paper is to introduce the method of RBF to‎ ‎an existing method in solving nonlinear two-level iterative‎ ‎techniques and also the method is implemented to four numerical‎ ‎examples‎. ‎The results reveal that the technique is very effective‎ ‎and simple. The main property of the method lies in its‎ ‎flexibility and ability to solve nonlinear equations accurately‎ ‎and conveniently.

In this paper, we are going to solve a class of ordinary differential equations that its source term are rational functions. We obtain the best approximation of source term by Chebyshev polynomials of the first kind, then we solve the ordinary differential equations by using the Adomian decomposition method

In the present paper, Radial Basis Function interpolations are applied to approximate a fuzzy function $tilde{f}:Rrightarrow mathcal{F}(R)$, on a discrete point set $X={x_1,x_2,ldots,x_n}$, by a fuzzy-valued function $tilde{S}$. RBFs are based on linear combinations of terms which include a single univariate function. Applying RBF to approximate a fuzzy function, a linear system will be obtained which by defining coefficient vector, target function will be approximated. Finally for showing the efficiency of the method we give some numerical examples.