International Journal of Industrial Mathematics
Volume:4 Issue: 4, Autumn 2012

In this paper, we propose a new approximate method, namely homotopy analysis sumudu transform method (HASTM) to solve various linear and nonlinear Fokker-Planck equations. The homotopy analysis sumudu transform method is a combined form of the sumudu transform method and the homotopy analysis method. The proposed technique finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. The results obtained by the proposed method show that the approach is very efficient, simple and can be applied to other nonlinear problems.

In the present study, it has been tried to show that to what extent the policy of the Govt. of India to promote the Private Higher Educational Institutions is feasible with the preamble of the constitution. A mathematical model and some suggestions for the remedy have been given in order to solve the problem.

Laminar free convection from a stretching cone embedded in the porous media with effects of pressure work, heat generation, thermal stratification and chemical reaction are considered. The governing partial differential equations have been transformed by a similarity transformation into a system of ordinary differential equations, which are solved numerically using a fourth order Runge-Kutta scheme with the shooting method. Solutions obtained in terms of local heat and mass transfer, velocity, temperature and concentration profiles for the values of physical parameters are displayed in both graphical and tabular forms.

Stochastic programming is an approach for modeling and solving optimization problem that include uncertain data. Chance constrained programming is one of the most important methods of stochastic programming. In many real world data envelopment analysis (DEA) models, exact amount of data can not be determined. Therefore several researchers proposed methods to evaluate stochastic efficiency of units with random inputs and/or outputs. Most of these methods are nonlinear. In this paper by introducing symmetric error structure for random variables, a linear from of stochastic CCR is provided. Finally, the proposed model is applied on an example.

In this paper, the focus is on additive models with interval data.An additive model can be converted to a multi-objective linear problem if information about preferences of the consumption of inputs and the production of outputs are taken into account. Here in this study, data are not exact and are of interval kind. Moreover, the most preferred solutions with available information by interval additive models are sought. It has also been shown that if additional information is available, an axial solution can be applied. Also, the most preferred target settings will be computed too. In this study twenty bank branches in Iran are evaluated, and target settings and efficiency are compared with the original case and significant decisions are made

In this paper, a new form of the homotopy perturbation method (NHPM) has been adopted for solving integro-differential equations. In the present study, firstly the NHPM is used to the integro-differential equation, which yields the Maclaurin series of the exact solution. By applying the Laplace transformation to the truncated Maclaurin series and then the Pad´e approximation to the solution derived from the Laplace transformation, we obtain mostly the exact solution of this kind of equations. Illustrative examples are given to represent the efficiency and the accuracy of the proposed method.

The inconsistent fuzzy linear matrix equations (shown as IFLME) of the form AXB = C for finding its fuzzy least squares solutions is studied in this paper. The AXB = C is rearranged with the kronecker product that was proposed by Allahviranloo et al. [8]. Then, by using the embedding approach, we extend it into a 2me × 2nr crisp system of linear equations and found its fuzzy least squares solutions. Also, sufficient condition for the existence of strong fuzzy least squares solutions are derived, and a numerical procedure for calculating the solutions is designed.

In this paper, we propose a novel approach for solving nonlinear interval Volterra integral equations (NIVIEs) based on the modifying Laplace decomposition method. We find the exact solutions of NIVIEs with less computation as compared with standard Laplace decomposition method, even there is no noise in the original problem. Finally, two illustrative examples have been solved to show the efficiency of the proposed method.

In this paper, the general Riccati differential equation is solved by using the Adomian’s decomposition method (ADM), modified Adomian’s decomposition method (MADM), variational iteration method (VIM), modified variational iteration method (MVIM), homotopy perturbation method (HPM), modified homotopy perturbation method (MHPM) and homotopy analysis method (HAM). The existence and uniqueness of the solution and convergence of the proposed methods are proved in details. A numerical example is studied to demonstrate the accuracy of the presented methods.

In this paper, we first of all define the distance measure entitled generalized Hausdorff distance between two trapezoidal generalized fuzzy numbers (TGFNs) that has been introduced by Chen [10]. Then using a other distance and combining with generalized Hausdorff distance, we define the similarity measure. The basic properties of the above mentioned similarity measure are proved in detail. Finally we rank two generalized fuzzy numbers using distance measure and similarity measure between them.