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Abstract: This paper investigates the problem of chaos and hyper-chaos control, and proposes a simple adaptive feedback control method for chaos control under a reasonable assumption. In comparison with previous methods, the present control technique is simple both in the form of the controller and its application. Several illustrative examples with numerical simulations are studied by using the results obtained in this paper. Study of examples shows that our control method works very well in chaos control. [Copyright &y& Elsevier]

Abstract: Recently, Shen et al. has published a paper concerning the properties and computations of matrix pseudospectra. However, some of the main results seem to be incomplete. As a complement of the paper, in this note we first make several examples to show the incompleteness of that results, then we give the modified results through giving more appropriate definitions replacing the one given in [Y. Shen, J. Zhao, H. Fan, Properties and computations of matrix pseudospectra, Applied Mathematics and Computation 161 (2005) 385–393]. An interesting inclusion theorem for pseudospectra is given, which provides preferable bounds for standard pseudospectra. Some other properties are also explored. [Copyright &y& Elsevier]

Abstract: In this paper, we are concerned with the oscillation of second order superlinear differential equations of the formA new oscillation criterion is established under quite general assumptions. Our results are based on the information on a sequence of subintervals of [t 0,∞) only, rather than on the whole half-line. Our methodology is somewhat different from that of previous authors . Our results generalize and extend some earlier results of Yu and Lu and Meng . An example is also given to illustrate the results. [Copyright &y& Elsevier]

Abstract: In this paper, Nicholson’s blowflies equation with diffusion and delay is investigated. By taking four different kinds of delay kernels and defining four corresponding characteristic equations, the existence of travelling wave solutions for Nicholson’ blowflies equation is obtained by employing the monotone iteration technique as well as the upper and lower solution method. [Copyright &y& Elsevier]

Abstract: This paper presents a common fixed point theorem for a family of R-weakly commuting mappings satisfying nonlinear type contractive conditions. This result improves and unifies previous results due to O’Regan and Saadati [D. O’Regan, R. Saadati, Nonlinear contraction theorems in probabilistic spaces, Appl. Math. Comput. 195 (2008) 86–93]. Also, the following results will be probabilistic versions and improvements of the results given in [D.W. Boyd, J.S.W. Wong, On nonlinear contractions, Proc. Am. Math. Soc. 20 (1969) 458–464; G. Jungck, Commuting maps and fixed points, Am. Math. Month. 83 (1976) 261–263; R.P. Pant, Common fixed points of noncommuting mappings, J. Math. Anal. Appl. 188 (1994) 436–440] and many other. [Copyright &y& Elsevier]

Abstract: In this paper, we present numerical analysis for the generalized quadrature rule for , where is an oscillatory function, and derive higher order generalized quadrature rules. The results show that the generalized quadrature rules are efficient for Bessel-trigonometric transformations and the accuracy increases when oscillation becomes faster. [Copyright &y& Elsevier]

Abstract: This paper presents new families of Newton-type iterative methods (Newton, Halley and Chebyshev methods) for finding simple zero of univariate non-linear equation, permitting in the vicinity of the root. Newton-type iterative methods have well-known geometric interpretation and admit their geometric derivation from a parabola. These algorithms are comparable to the well-known powerful classical methods of Newton, Halley and Chebyshev respectively, and these can be seen as special cases of these families. The efficiency of the presented methods is demonstrated by numerical examples. [Copyright &y& Elsevier]

Abstract: In this paper, we suggest and analyze a new three-step iterative method for solving nonlinear equations involving only first derive of the function using a new decomposition technique which is due to Noor [M. Aslam Noor, Numerical Analysis and Optimization, Lecture Notes, COMSATS Institute of Information Technology, Islamabad, Pakistan, 2006; M. Aslam Noor, New iterative schemes for nonlinear equations, Appl. Math. Comput., in press] and Noor and Noor [M. Aslam Noor, K. Inayat Noor, Some iterative schemes for nonlinear equations, Appl. Math. Comput., in press]. We show that this new iterative method has fourth-order convergence. Several numerical examples are given to illustrate the efficiency and performance of the new method. [Copyright &y& Elsevier]

Abstract: In this paper, by using the theories and methods of mathematical analysis and computer algebra, a reliable algorithm of finite difference method for solving singular perturbation problems was established, a new matlab procedure ehssp was implemented, too. Several linear and non-linear problems are presented to illustrate the implementation of the program. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce and analyze the continuous finite element method for a class of delay-differential equation with a variable term. At first for the case of the constant delay and based on an orthogonal expansion in an element we derive optimal superconvergence u − U =O(h p+2), p ⩾2 at the (p +1)-order Lobatto points and u − U =O(h 2p ) at the integer nodal points. Next we prove the stability of linear and quadratic finite element schemes for the case of constant delay. For the case of variable delay, by use of the approximative to the continuous delay in every subinterval we decompose the original problem into a series of subproblems with constant delay. Finally we give a recursive schemes which can be compute by every subproblem. [Copyright &y& Elsevier]

Abstract: By means of variational iteration method the solution of generalized Huxley equation are obtained, comparison with the Adomian decomposition method is made, showing that the former is more effective than the later. In this paper, He’s variational iteration method is introduced to overcome the difficulty arising in calculating Adomian polynomials. [Copyright &y& Elsevier]

Abstract: This paper provides a method for the decomposition of total factor productivity into partial measures of productivity. The proposed decomposition model measures the capacity productivity change and variable input productivity change. The latter can further be decomposed into partial factor technical efficiency change and partial factor technical change. This new decomposition isolates various sources of total factor productivity, and avoids providing a misleading indication of overall productivity. [Copyright &y& Elsevier]

Abstract: Analytic Hierarchy Process is a well-known method that is only able to rank different alternatives according to their AHP weights, but it does not determine the necessary threshold for discriminate between acceptable and unacceptable alternatives. In the other words, it does not lead the DM to choose the alternatives that have higher weights than the threshold. In this paper, we introduce a new method by which we are able to accept/reject alternatives based on AHP weights. The proposed method determines the necessary threshold by comparing the anticipated status with the desired status of alternatives and using LP and AHP combination for it. [Copyright &y& Elsevier]

Abstract: In this paper, we provide a new meshless Petrov-Galerkin method, in which the trial space is generated by the global supported RBFs, the test space is generated by the compactly supported RBFs. The theoretical analysis and numerical results indicate that it is an efficient and accurate numerical method. [Copyright &y& Elsevier]

Abstract: A new third-order multipoint method without using second derivative for finding simple zeros of non-linear functions, permitting f′(x)=0 in the vicinity of the required root is presented in this paper. Furthermore, numerical tests supporting the theory and comparison of the results with respect to the existing classical methods are also given. [Copyright &y& Elsevier]

Abstract: In this paper, for the nonlinear diffusion model of image denoising and segmentation, we present two high-order explicit algorithms and a semi-implicit algorithm using algebraic multi-grid method. The unconditional stability of the semi-implicit approximation is given. The numerical results of the above three algorithms are demonstrated with comparison to general explicit algorithm in [Y. Chen, B.C. Vemuri, L. Wang, Image denoising and segmentation via nonlinear diffusion, Comput. Math. Appl. 39 (2000) 131–149] for real noised images. The numerical results show that the implicit algorithm is quicker and sharper than all explicit algorithms. [Copyright &y& Elsevier]

Abstract: In this paper, numerical solution of first-order systems of ordinary differential equations (ODEs) is considered and an error estimation method is proposed. By this method, the efficiency of pseudospectral method to solve the systems is determined and a modified pseudospectral method is presented. Furthermore, with providing some examples, the aforementioned cases are dealt with numerically. [Copyright &y& Elsevier]

Abstract: In this paper, a method of lines is proposed for solving partial differential equations. A suitable spatial discretisation is introduced, then the numerical examples show that the method of lines is feasible and very effective for solving parabolic problems. [Copyright &y& Elsevier]

Abstract: In this paper, a numerical solution of an inverse non-dimensional heat conduction problem will be considered. By using a sensor located at a point inside the body and measuring the temperature at a point x = x 1, 0< x 1 <1, and applying finite difference method to the inverse heat conduction problem, we determine a stable numerical solution to this problem. [Copyright &y& Elsevier]