Journal of Difference Equations http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Application of Hybrid Functions for Solving Duffing-Harmonic Oscillator Thu, 14 Aug 2014 07:09:07 +0000 http://www.hindawi.com/journals/jde/2014/210754/ A numerical method for finding the solution of Duffing-harmonic oscillator is proposed. The approach is based on hybrid functions approximation. The properties of hybrid functions that consist of block-pulse and Chebyshev cardinal functions are discussed. The associated operational matrices of integration and product are then utilized to reduce the solution of a strongly nonlinear oscillator to the solution of a system of algebraic equations. The method is easy to implement and computationally very attractive. The results are compared with the exact solution and results from several recently published methods, and the comparisons showed proper accuracy of this method. Mohammad Heydari, Ghasem Brid Loghmani, Seyed Mohammad. Hosseini, and Seyed Mehdi Karbassi Copyright © 2014 Mohammad Heydari et al. All rights reserved. Almost Periodic Solution of a Discrete Schoener’s Competition Model with Delays Thu, 24 Jul 2014 08:40:44 +0000 http://www.hindawi.com/journals/jde/2014/256094/ We consider an almost periodic discrete Schoener’s competition model with delays. By means of an almost periodic functional hull theory and constructing a suitable Lyapunov function, sufficient conditions are obtained for the existence of a unique strictly positive almost periodic solution which is globally attractive. An example together with numerical simulation indicates the feasibility of the main result. Hui Zhang, Yingqi Li, Bin Jing, Xiaofeng Fang, and Jing Wang Copyright © 2014 Hui Zhang et al. All rights reserved. Exact Controllability of an Impulsive Semilinear System with Deviated Argument in a Banach Space Wed, 16 Jul 2014 00:00:00 +0000 http://www.hindawi.com/journals/jde/2014/461086/ A functional differential equation with deviated argument coupled with impulsive conditions is studied for the existence and uniqueness of the mild solution and exact controllability of the system. The results are obtained by using Banach contraction principle and semigroup theory without imposing additional assumptions such as analyticity and compactness conditions on the generated semigroup and the nonlinear term. An example is provided to illustrate the presented theory. Sanjukta Das, Dwijendra N. Pandey, and N. Sukavanam Copyright © 2014 Sanjukta Das et al. All rights reserved. Hermite Wavelet Method for Fractional Delay Differential Equations Wed, 02 Jul 2014 09:09:44 +0000 http://www.hindawi.com/journals/jde/2014/359093/ We proposed a method by utilizing method of steps and Hermite wavelet method, for solving the fractional delay differential equations. This technique first converts the fractional delay differential equation to a fractional nondelay differential equation and then applies the Hermite wavelet method on the obtained fractional nondelay differential equation to find the solution. Several numerical examples are solved to show the applicability of the proposed method. Umer Saeed and Mujeeb ur Rehman Copyright © 2014 Umer Saeed and Mujeeb ur Rehman. All rights reserved. Rate of Convergence of Modified Baskakov-Durrmeyer Type Operators for Functions of Bounded Variation Wed, 02 Jul 2014 00:00:00 +0000 http://www.hindawi.com/journals/jde/2014/235480/ We study a certain integral modification of well-known Baskakov operators with weight function of beta basis function. We establish rate of convergence for these operators for functions having derivative of bounded variation. Also, we discuss Stancu type generalization of these operators. Prashantkumar Patel and Vishnu Narayan Mishra Copyright © 2014 Prashantkumar Patel and Vishnu Narayan Mishra. All rights reserved. Global Asymptotic Stability for Linear Fractional Difference Equation Tue, 01 Jul 2014 07:55:35 +0000 http://www.hindawi.com/journals/jde/2014/275312/ Consider the difference equation ,  , where all parameters ,  , and the initial conditions ,   are nonnegative real numbers. We investigate the asymptotic behavior of the solutions of the considered equation. We give easy-to-check conditions for the global stability and global asymptotic stability of the zero or positive equilibrium of this equation. A. Brett, E. J. Janowski, and M. R. S. Kulenović Copyright © 2014 A. Brett et al. All rights reserved. A Remark on the Regularity Criterion for the MHD Equations via Two Components in Morrey-Campanato Spaces Wed, 25 Jun 2014 11:18:10 +0000 http://www.hindawi.com/journals/jde/2014/364269/ We consider the regularity criterion for the 3D MHD equations. It is proved that if the horizontal components of the velocity and magnetic fields satisfy with , then the solution smooth. This improves the result given by Gala (2012). Zujin Zhang, Tong Tang, and Fumin Zhang Copyright © 2014 Zujin Zhang et al. All rights reserved.