INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS
Year:2012 | Volume:4 | Issue:1|Papers Count:7

This paper deals with the implementation of Haar wavelets to solve the optimal control problem of linear time-varying singular systems with a quadratic cost functional. The properties of Haar Wavelets are presented. The state variable, state rate and the control vector are expanded in Haar orthogonal basis with unknown coefficients. The relation between the coefficients of the state rate and state variable is provided and the necessary condition of optimality is derived as a linear system of algebraic equations in terms of the unknown coefficients of the state and control vectors. Illustrative example is included to demonstrate the validity and applicability of the technique.

In this paper, we present an improved method for solving Riccati equations. This modification is based on the previous scheme to obtain the approximate solution of Riccati equations [B.Q. Tang and X.F. Li, A new method for determining the solution of Riccati differential equations, Appl. Math. Comput. 194 (2007) 431-440]. Some numerical illustrations are given to show the effectiveness and high accuracy of the proposed modification.

Using fuzzy Laplace transform method, the solution of fuzzy convolution Volterra integral equation (FCVIE) of the second kind with convolution fuzzy and crisp kernel is investigated. So, fuzzy convolution operator is proposed and related theorem is submitted which is useful for solving FCVIEs. Finally, several illustrative examples with fuzzy and crisp convolution kernels are given to show the ability of the proposed method.

Different processes in Decision Making Unit (DMU) are the same as sub processes in that DMU when it is not considered as black box. Most of the time these sub processes are mooted in a series structure and frequently used in real world applications. When it is aimed to evaluate the performance of a unit with its sub processes and what it did in the past, those techniques which show progress and regress can be used. One of these famous techniques is Malmquisr Productivity Index (MPI). Here MPI is developed and used for series structural DMUs, with two components, in which intermediate inputs and outputs exist.

In this paper, the weakly singular nonlinear integro-differential equation is solved by using the homotopy perturbation and homotopy analysis methods. The approximation solution of this equation is calculated in the form of a series which its components are computed easily. The existence and uniqueness of the solution and the convergence of the proposed method are proved. A numerical example is studied to demonstrate the accuracy of the presented method.

Integral equations have many applications in the theory of elasticity, engineering, mathematical physics, potential theory, electrostatic and radiative heat transfer problems. In this paper, we present a method for solving fuzzy linear Fredholm integral equations of the second kind, namely “homotopy analysis method” (HAM). It is found that the HAM provides us with a simple way to adjust and control the convergence region of solution series by introducing convergence-control parameter h, which is the main advantage of this method.

In this paper, we will investigate existence and uniqueness of solution of fuzzy Volterra integral equation of the second kind.