INTERNATIONAL JOURNAL OF MATHEMATICAL MODELLING & COMPUTATION
Year:2015 | Volume:5 | Issue:1|Papers Count:8

A Class of new methods based on a septic non-polynomial spline function for the numerical solution of problems in calculus of variations is presented. The local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th. are obtained. The inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. Convergence analysis of these methods is discussed. Numerical results are given to illustrate the efficiency of methods and compared with the methods in [23, 32-34].

We study the convergence of the modified Noor iterative scheme for the class of asymptotically pseudocontractive mappings in the intermediate sense which is not necessarily Lipschitzian. Our results improves, extends and unifies the results of [Schu, Iterative construction of fixed points of asymptotically nonexpansive mappings, Mathematical Analysis and Applications, 158 (2) (1991) 407-413] and [Qin et al. Convergence theorems on asymptotically pseudocontractive mappings in the intermediate sense, Fixed Point Theory and Applications, 2010, Article ID 186874, 14 pages, (2010)].

This paper analyzes a controllable discrete-time machine repair problem with L operating machines and two technicians. The number of working servers can be adjusted depending on the number of failed machines in the system one at a time at machine's failure or at service completion epochs. Analytical closed-form solutions of the stationary probabilities of the number of failed machines in the system are obtained. We develop the total expected cost function per machine per unit time and obtain the optimal operating policy and the optimal service rate at minimum cost using quadratic t search method and simulated annealing method. Various performance measures along with numerical results to illustrate the influence of various parameters on the buffer behavior are also presented.

In this work, we propose a modification of Steensen’s method with some free parameters. These parameters are then be used for further acceleration via the concept of with memorization. In this way, we derive a fast Steensen-type method with memory for solving nonlinear equations. Numerical results are also given to support the underlying theory of the article.

A single server provides service to all arriving customers with service time following general distribution. After every service completion the server has the option to leave for phase one vacation of random length with probability p or continue to stay in the system with probability 1-p. As soon as the completion of phase one vacation, the server may take phase two vacation with probability q or to remain in the system with probability 1-q, after phase two vacation again the server has the option to take phase three vacation with probability r or to remain in the system with probability 1-r. The vacation times are assumed to be general. The server is interrupted at random and the duration of attending interruption follows exponential distribution. Also we assume, the customer whose service is interrupted goes back to the head of the queue where the arrivals are Poisson. The time dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results have been obtained explicitly. Also the mean number of customers in the queue and system and the waiting time in the queue and system are also derived. Particular cases and numerical results are discussed.

The computation of the inverse roots of matrices arises in evaluating unsymmetric eigenvalue problems, solving nonlinear matrix equations, computing some matrix functions, control theory and several other areas of applications. It is possible to approximate the matrix inverse pth roots by exploiting a specialized version of Newton's method, but previous researchers have mentioned that some iterations have poor convergence and stability proper- ties. In this work, a stable recursive technique to evaluate an inverse pth root of a given matrix is presented. The scheme is analyzed and its properties are investigated. Computational experiments are also performed to illustrate the strengths and weaknesses of the proposed method.

In this paper, the dierential transformation method (DTM) is applied to solve fuzzy fractional heat equations. The elementary properties of this method are given. The approximate and exact solutions of these equations are calculated in the form of series with easily computable terms. The proposed method is also illustrated by some examples. The results reveal that DTM is a highly eective scheme for obtaining approximate analytical solutions of fuzzy fractional heat equations.

This paper presents a Taylor series approach for solving linear fractional decentralized bi-level multi-objective decision-making (LFDBL-MODM) problems with a single decision maker at the upper level and multiple decision makers at the lower level. In the pro- posed approach, the membership functions associated with each objective (s) of the level (s) of LFDBL-MODM are transformed to a linear form by using a Taylor series and then they are unified. On using the Kuhn-Tucker conditions, the problem is finally reduced to a single objective. Numerical example is given in order to illustrate the efficiency and superiority of the proposed approach.