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Uses the continuous Legendre wavelets on the interval [0,1) in the manner of M. Razzaghi and S. Yousefi, to solve the linear second kind integral equations. We use quadrature formula for the calculation of inner products of any functions, which are required in the approximation for the integral equations. Then, we reduced the integral equation to the solution of linear algebraic equations.

The main purpose of this paper is to implement the piecewise spectral-variational iteration method (PSVIM) to solve the nonlinear Lane-Emden equations arising in mathematical physics and astrophysics.

This method is based on a combination of Chebyshev interpolation and standard variational iteration method (VIM) and matching it to a sequence of subintervals. Unlike the spectral method and the VIM, the proposed PSVIM does not require the solution of any linear or nonlinear system of equations and analytical integration.

Some well-known classes of Lane-Emden type equations are solved as examples to demonstrate the accuracy and easy implementation of this technique.

In this paper, a new and efficient technique is proposed to solve the nonlinear Lane-Emden equations. The proposed method overcomes the difficulties arising in calculating complicated and time-consuming integrals and terms that are not needed in the standard VIM.

In this paper, a new semi analytic technique namely the Homotopy Analysis Method (HAM) is applied for SEIR Epidemic model. HAM is different from already existing perturbation methods, and is most suitable for strongly non linear simultaneous differential equations arising in this model. The advantage of this method is that it provides a direct scheme for solving the problem, i.e. without the need for linearization, perturbation, massive computation and any transformation. MATHEMATICA 8.0 is used to carry out computations. Results were discussed graphically, for four childhood diseases.

In this paper, the authors extend the goal-directed benchmarking theory proposed by Stewart for benchmarking and selecting suppliers. This extension is in recognition of the fact that benchmarking for suppliers is more than a pure monitoring process and includes a component of future planning. The paper aims to discuss these issues.

In this paper, the proposed model utilizes a goal programming structure to find points on the efficient frontier which are realistically attainable by suppliers in the presence of undesirable outputs, but at the same time achieving a closer method to long-term organizational goals (as distinct from the local performance of individual suppliers).

The contributions of the current paper are as follows: the proposed model considers undesirable outputs in the context of goal-directed benchmarking. The proposed model does not demand weights from the decision maker. The proposed model can be easily computerized, enabling it to serve as a decision making tool to assist decision makers. For the first time, the proposed model is applied for the supplier selection and benchmarking.

To the best of knowledge of the authors, there is not any reference that discusses supplier selection problem and benchmarking in the presence of undesirable outputs in the context of goal-directed benchmarking.