International Journal of Mathematical Modeling & Computations: 1 (1)

Open Access Article

1 - NON-POLYNOMIAL SPLINE FOR THE NUMERICAL SOLUTION OF PROBLEMS IN CALCULUS OF VARIATIONS
Reza Jalilian J. Rashidinia K. Farjian H. Jalilian

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 s More

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 eciency of methods and compared with the methods in [28-32]. Manuscript profile

Open Access Article

2 - CONVERGENCE THEOREMS FOR ASYMPTOTICALLY PSEUDOCONTRACTIVE MAPPINGS IN THE INTERMEDIATE SENSE FOR THE MODIFIED NOOR ITERATIVE SCHEME
Godwin Amechi Okeke Johnson O Olaleru

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 [23] and Qin {\it et More

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 [23] and Qin {\it et al.} [25]. Manuscript profile

Open Access Article

3 - ANALYSIS OF DISCRETE-TIME MACHINE REPAIR PROBLEM WITH TWO REMOVABLE SERVERS UNDER TRIADIC POLICY
Veena Goswami P. Vijaya Laxmi

This paper analyzes a controllable discrete-time machine repair problem withL operating machines and two repairmen. The number of working servers can be adjusteddepending on the number of failed machines in the system one at a time at machine's failure orat service comp More

This paper analyzes a controllable discrete-time machine repair problem withL operating machines and two repairmen. The number of working servers can be adjusteddepending on the number of failed machines in the system one at a time at machine's failure orat service completion epochs. Analytical closed-form solutions of the stationary probabilities ofthe number of failed machines in the system are obtained. We develop the total expected costfunction per machine per unit time and obtain the optimal operating policy and the optimalservice rate at minimum cost using quadratic ¯t search method and simulated annealingmethod. Various performance measures along with numerical results to illustrate the in°uenceof various parameters on the bu®er behavior are also presented. Manuscript profile

Open Access Article

4 - A MODIFIED STEFFENSEN'S METHOD WITH MEMORY FOR NONLINEAR EQUATIONS
Farhad Khaksar Haghani

In this note, we propose a modification of Steffensen'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 Steffensen-type method with memory for solving nonlin More

In this note, we propose a modification of Steffensen'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 Steffensen-type method with memory for solving nonlinear equations. Numerical results are also given to support the underlying theory of the article. Manuscript profile

Open Access Article

5 - A NON-MARKOVIAN BATCH ARRIVAL QUEUE WITH SERVICE INTERRUPTION AND EXTENDED SERVER VACATION
G. Ayyappan K. Sathiya

A single server provides service to all arriving customers with servicetime following general distribution. After every service completion theserver has the option to leave for phase one vacation of random lengthwith probability p or continue to stay in the system with More

A single server provides service to all arriving customers with servicetime following general distribution. After every service completion theserver has the option to leave for phase one vacation of random lengthwith probability p or continue to stay in the system with probability1 􀀀 p. As soon as the completion of phase one vacation, the servermay take phase two vacation with probability q or to remain in thesystem with probability 1􀀀q, after phase two vacation again the serverhas the option to take phase three vacation with probability r or toremain in the system with probability 1 􀀀 r. The vacation times areassumed to be general. The server is interrupted at random and theduration of attending interruption follows exponential distribution. Alsowe assume, the customer whose service is interrupted goes back to thehead of the queue where the arrivals are Poisson. The time dependentprobability generating functions have been obtained in terms of theirLaplace transforms and the corresponding steady state results have beenobtained explicitly. Also the mean number of customers in the queueand system and the waiting time in the queue and system are alsoderived. Particular cases and numerical results are discussed. Manuscript profile

Open Access Article

6 - A STABLE COUPLED NEWTON'S ITERATION FOR THE MATRIX INVERSE $P$-TH ROOT
Amir Sadeghi

The computation of the inverse roots of matrices arises in evaluating non-symmetriceigenvalue problems, solving nonlinear matrix equations, computing some matrixfunctions, control theory and several other areas of applications. It is possible toapproximate the matrix in More

The computation of the inverse roots of matrices arises in evaluating non-symmetriceigenvalue problems, solving nonlinear matrix equations, computing some matrixfunctions, control theory and several other areas of applications. It is possible toapproximate the matrix inverse pth roots by exploiting a specialized version of New-ton's method, but previous researchers have mentioned that some iterations havepoor convergence and stability properties. In this work, a stable recursive techniqueto evaluate an inverse pth root of a given matrix is presented. The scheme is analyzedand its properties are investigated. Computational experiments are also performedto illustrate the strengths and weaknesses of the proposed method. Manuscript profile

Open Access Article

7 - DIFFERENTIAL TRANSFORMATION METHOD FOR SOLVING FUZZY FRACTIONAL HEAT EQUATIONS
Bahman Ghazanfari Parvin Ebrahimi

In this paper, the differential transformation method (DTM) was applied to solve fuzzy fractional heat equations. The elementary properties of this method were given. The approximate and exact solutions of these equations were calculated in the form of series with easil More

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

Open Access Article

8 - A TAYLOR SERIES APPROACH FOR SOLVING LINEAR FRACTIONAL DECENTRALIZED BI-LEVEL MULTI-OBJECTIVE DECISION-MAKING UNDER FUZZINESS
Mansour Saraj Nima Safaei

This paper presents a Taylor series approach for solving linear fractional de-centralized bi-level multi-objective decision-making (LFDBL-MODM) problems with asingle decision maker at the upper level and multiple decision makers at the lower level.In the proposed approa More

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

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