مجله بین المللی محاسبات و مدل سازی ریاضی
سال پنجم شماره 4 (Autumn 2015)

This paper present a novel numerical algorithm for the linear one- dimensional heat and wave equation. In this method, a nite dierence approach had been used to discrete the time derivative while cubic spline is applied as an interpolation function in the space dimension. We discuss the accuracy of the method by expanding the equation based on Taylor series and minimize the error. The proposed method has eighth-order accuracy in space and fourth-order accuracy in time variables. From the computational point of view, the solution obtained by this method is in excellent agreement with those obtained by previous works and also it is ecient to use. Numerical examples are given to show the applicability and eciency of the method.

In this paper, we have proposed a study on controllability and optimal harvesting of a prey predator model and mathematical non linear formation of the equation equilibrium point of Routh harvest stability analysis. The problem of determining the optimal harvest policy is solved by invoking Pontryagin0s maximum principle dynamic optimization of the harvest policy is studied by taking the combined harvest eect as a dynamics variable

The aim of this paper is to design a Fractional Order Sliding Mode Controllers (FOSMC) for a class of DC-DC converters such as boost and buck converters. Firstly, the control law is designed with respect to the properties of fractional calculus, the design yields an equiv-alent control term with an addition of discontinuous (attractive) control law. Secondly, the mathematical proof of the stability condition and convergence of the proposed fractional order sliding surface is presented. Finally the effectiveness and robustness of the proposed ap-proaches compared with classical SMCs are demonstrated by simulation results with different cases.

In this paper, the nonlinear differential equation for the convection of the temperature distribution of a straight fin with the thermal conductivity depends on the temperature is solved using Adomian Decomposition Method and Padé approximation(PADM) for boundary problems. Actual results are then compared with results obtained previously using digital solution by Runge–Kuttamethod and a differential transformation method (DTM) in order toverify the accuracy of the proposed method.

The present article deals with the inter specific competition and intra-specific competition among predator populations of a prey-dependent three component food chain model consisting of two competitive predator sharing one prey species as their food. The behaviour of the system near the biologically feasible equilibria is thoroughly analyzed. Boundedness and dissipativeness of the system are established. Stability analysis including local and global stability of the equilibria has been carried out in order to examine the dynamic behaviour of the system. The present system experiences Hopf-Andronov bifurcation for suitable choice of parameter values. As a result, intra-specific competition among predator populations can be beneficial for the survival of predator. The ecological implications of both the analytical and numerical findings are discussed at length towards the end.

In this paper, we introduce an efficient method based on Haar wavelet to approximate a solution for the two-dimensional linear stochastic Fredholm integral equation. We also give an example to demonstrate the accuracy of the method.