International Journal of Mathematical Modeling & Computations: 1 (3)

Open Access Article

1 - APPLICATION OF DIFFERENTIAL TRANSFORM METHOD TO SOLVE HYBRID FUZZY DIFFERENTIAL EQUATIONS
Mahmoud Paripour Homa Heidari Elahe Hajilou

In this paper, we study the numerical solution of hybrid fuzzy differential equations by using differential transformation method (DTM). This is powerful method which consider the approximate solution of a nonlinear equation as an infinite series usually converging to t More

In this paper, we study the numerical solution of hybrid fuzzy differential equations by using differential transformation method (DTM). This is powerful method which consider the approximate solution of a nonlinear equation as an infinite series usually converging to the accurate solution. Several numerical examples are given and by comparing the numerical results obtained from DTM and predictor corrector method (PCM), we have studied their accuracy. Manuscript profile

Open Access Article

2 - SOLVING NONLINEAR TWO-DIMENSIONAL VOLTERRA INTEGRAL EQUATIONS OF THE FIRST-KIND USING BIVARIATE SHIFTED LEGENDRE FUNCTIONS
Somayeh Nemati Y. Ordokhani

In this paper, a method for ﬁnding an approximate solution of a class of two-dimensional nonlinear Volterra integral equations of the ﬁrst-kind is proposed. This problem is transformedto a nonlinear two-dimensional Volterra integral equation of the second-kind. The prop More

In this paper, a method for ﬁnding an approximate solution of a class of two-dimensional nonlinear Volterra integral equations of the ﬁrst-kind is proposed. This problem is transformedto a nonlinear two-dimensional Volterra integral equation of the second-kind. The properties ofthe bivariate shifted Legendre functions are presented. The operational matrices of integrationtogether with the product operational matrix are utilized to reduce the solution of the second-kind equation to the solution of a system of linear algebraic equations. Finally, a system of nonlinear algebraic equations is obtained to give an approximate solution of the main problem.Also, numerical examples are included to demonstrate the validity and applicability of themethod. Manuscript profile

Open Access Article

3 - AN M/G/1 QUEUE WITH REGULAR AND OPTIONAL PHASE VACATION AND WITH STATE DEPENDENT ARRIVAL RATE
Rathinasabapathy Kalyanaraman Shanthi R

We consider an M/G/1 queue with regular and optional phase vacation and withstate dependent arrival rate. The vacation policy is after completion of service if there areno customers in the system, the server takes vacation consisting of K -phases, each phaseis generally More

We consider an M/G/1 queue with regular and optional phase vacation and withstate dependent arrival rate. The vacation policy is after completion of service if there areno customers in the system, the server takes vacation consisting of K -phases, each phaseis generally distributed. Here the first phase is compulsory where as the other phases areoptional. For this model the supplementary variable technique has been applied to obtainthe probability generating functions of number of customers in the queue at the different server states. Some particular models are obtained and a numerical study is also carriedout. Manuscript profile

Open Access Article

4 - A NOTE ON "A SIXTH ORDER METHOD FOR SOLVING NONLINEAR EQUATIONS"
Paria Assari Taher Lotfi

In this study, we modify an iterative non-optimal without memory method, in such a way that is becomes optimal. Therefore, we obtain convergence order eight with the some functional evaluations. To justify our proposed method, some numerical examples are given.

In this study, we modify an iterative non-optimal without memory method, in such a way that is becomes optimal. Therefore, we obtain convergence order eight with the some functional evaluations. To justify our proposed method, some numerical examples are given. Manuscript profile

Open Access Article

5 - A STRONG COMPUTATIONAL METHOD FOR SOLVING OF SYSTEM OF INFINITE BOUNDARY INTEGRO-DIFFERENTIAL EQUATIONS
M. Matinfar Abbas Riahifar H. Abdollahi

The introduced method in this study consists of reducing a system of infinite boundary integro-differential equations (IBI-DE) into a system of al- gebraic equations, by expanding the unknown functions, as a series in terms of Laguerre polynomials with unknown coeffi More

The introduced method in this study consists of reducing a system of infinite boundary integro-differential equations (IBI-DE) into a system of al- gebraic equations, by expanding the unknown functions, as a series in terms of Laguerre polynomials with unknown coefficients. Properties of these polynomials and operational matrix of integration are rst presented. Finally, two examples illustrate the simplicity and the effectiveness of the proposed method have been presented. Manuscript profile

Open Access Article

6 - NON-STANDARD FINITE DIFFERENCE METHOD FOR NUMERICAL SOLUTION OF SECOND ORDER LINEAR FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS
Pramod Kumar Pandey

In this article we have considered a non-standard finite difference method for the solution of second order Fredholm integro differential equation type initial value problems. The non-standard finite difference method and the composite trapezoidal quadrature method is u More

In this article we have considered a non-standard finite difference method for the solution of second order Fredholm integro differential equation type initial value problems. The non-standard finite difference method and the composite trapezoidal quadrature method is used to transform the Fredholm integro-differential equation into a system of equations. We have also developed a numerical method for the numerical approximation of the derivative of the solution of the problems. The numerical results in experiment on some model problems show the simplicity and efficiency of the method. Numerical results showed that the proposed method is convergent and at least second order of accurate. Manuscript profile

Open Access Article

7 - OPTIMUM GENERALIZED COMPOUND LINEAR PLAN FOR MULTIPLE-STEP STEP-STRESS ACCELERATED LIFE TESTS
Navin Chandra Mashroor Ahmad Kha

In this paper, we consider an i.e., multiple step-stress accelerated life testing (ALT) experiment with unequal duration of time . It is assumed that the time to failure of a product follows Rayleigh distribution with a log-linear relationship between stress and lifetim More

In this paper, we consider an i.e., multiple step-stress accelerated life testing (ALT) experiment with unequal duration of time . It is assumed that the time to failure of a product follows Rayleigh distribution with a log-linear relationship between stress and lifetime and also we assume a generalized Khamis-Higgins model for the effect of changing stress levels. Taking into account that the problem of choosing the optimal time for 3-step step-stress tests under compound linear plan was initially attempted by Khamis and Higgins [16]. We ever first have developed a generalized compound linear plan for multiple-step step-stress setting using variance-optimality criteria. Some numerical examples are discussed to illustrate the proposed procedures. Manuscript profile

Open Access Article

8 - EFFECT OF COUNTERPROPAGATING CAPILLARY GRAVITY WAVE PACKETS ON THIRD ORDER NONLINEAR ‎‎E‎VOLUTION EQUATIONS IN THE PRESENCE OF WIND FLOWING OVER WATER
A. K. Dhar Joydev Mondal

Asymptotically exact and nonlocal third order nonlinear evolution equations are derivedfor two counterpropagating surface capillary gravity wave packets in deep water in thepresence of wind flowing over water.From these evolution equations stability analysis ismade for More

Asymptotically exact and nonlocal third order nonlinear evolution equations are derivedfor two counterpropagating surface capillary gravity wave packets in deep water in thepresence of wind flowing over water.From these evolution equations stability analysis ismade for a uniform standing surface capillary gravity wave trains for longitudinal perturbation. Instability condition is obtained and graphs are plotted for maximum growth rateof instability and for wave number at marginal stability against wave steepness for some different values of dimensionless wind velocity. Manuscript profile

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