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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]

Finding the solution of the absolute value equation (AVE) A x − | x | = b has attracted much attention in recent years. In this paper, we propose a relaxed nonlinear PHSS-like iterative method, which is more efficient than the Picard-HSS iterative method for the AVE, and is a generalization of the nonlinear HSS-like iteration method for the AVE. By using the theory of nonsmooth analysis, we prove the convergence of the relaxed nonlinear PHSS-like iterative method for the AVE. Numerical experiments are given to demonstrate the feasibility, robustness and effectiveness of the relaxed nonlinear HSS-like method. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concern analytic solutions of an iterative functional equation of the formByconstructing a convergent power series solution of an auxiliary equationanalytic solutions of the original equation are obtained. We discuss not only these α appeared in the auxiliary equation at the hyperbolic case 0<∣α∣≠1 and resonance, i.e., at a root of the unity, but also those α near resonance (i.e., near a root of the unity) under Brjuno condition. [Copyright &y& Elsevier]

Abstract: In [Z.Wei, S. Yao, L. Liu, The convergence properties of some new conjugate gradient methods, Applied Mathematics and Computation 183 (2006) 1341–1350], Wei et al. proposed a new conjugate gradient method called WYL method which has good numerical experiments and some excellent properties such as . In this paper, we prove that while , the sufficient descent condition can be satisfied at each iteration of the WYL method. Based on this, the global convergence of the WYL method with the standard Armijo line search and the generalized Wolfe–Powell line search is established. [Copyright &y& Elsevier]

Abstract: This paper studies the Zakharov equation with power law nonlinearity. An exact 1-soliton solution is obtained by the ansatz method. The parameter regimes are identified in the process. The numerical simulation is also given to complete the study. [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: The aim of this paper is to point out that the integer programming model proposed by Eren and Güner [T. Eren, E. Güner, A bicriteria flowshop scheduling problem with setup times, Appl. Math. Comput. 183 (2006) 1292–1300] is incorrect. We propose a new integer programming model for the same scheduling problem based on their model. [Copyright &y& Elsevier]

Abstract: The C-Algorithm introduced in is designed to determine isochronous centers for Lienard-type differential systems, in the general real analytic case. However, it has a large complexity that prevents computations, even in the quartic polynomial case. The main result of this paper is an efficient algorithmic implementation of C-Algorithm, called ReCA (Reduced C-Algorithm). Moreover, an adapted version of it is proposed in the rational case. It is called RCA (Rational C-Algorithm) and is widely used in to find many new examples of isochronous centers for the Liénard type equation. [Copyright &y& Elsevier]

Abstract: In this paper, we present some new variants of super-Halley method for solving nonlinear equations. These methods are free from second derivatives and require one function and two first derivative evaluations per iteration. Analysis of convergence shows that the methods are fourth-order. Several numerical examples are given to illustrate the performance of the presented methods. [Copyright &y& Elsevier]

Abstract: In this paper, two one-parameter families of irrational and rational iterative methods for solving nonlinear equations are constructed. The construction of the iterative process is based on one-point approximation by the quadratic equation . Euler, Chebyshev, Halley, Super-Halley methods can be seen as the special cases of the family. And by analysis of asymptotic errors, we prove the two families are all cubically convergent. Furthermore, the rational iterative family can be extended to Banach spaces easily. [Copyright &y& Elsevier]

Abstract: In this paper, a bilevel time minimizing assignment problem is studied in which the aim is to find an optimal partition of the set of n facilities into two mutually disjoint subsets L 1 and L 2 where, L 1 contains m facilities called Level-I facilities and L 2 contains the remaining (n − m) facilities termed as Level-II facilities. The partition is to be optimal in the sense that for this partition the sum of the completion times of the jobs assigned to Level-I and Level-II facilities is the least. It is assumed that all the jobs are to be done, each facility works only on one job, and on each job only one facility works. Further Level-II facilities start working simultaneously on their respective assigned jobs only after Level-I facilities, working in parallel, have finished their jobs. For a feasible assignment denotes the completion time of the jobs assigned to Level-I facilities and that of the jobs assigned to Level-II facilities. Depending on m is greater or smaller than (n − m), the pairs of the type and of the completion times of the jobs assigned to Level-I and Level-II facilities are generated and an optimal partition of the set of n facilities is determined corresponding to the pair for which is the least. To obtain the global minimizer of the proposed problem, a polynomial time algorithm is presented which has been coded in C++ and an empirical analysis has been carried out with the help of randomly generated test problems. [Copyright &y& Elsevier]

Abstract: In this paper, we use power series method to solve stiff ordinary differential equations of the first order and an ordinary differential equation of any order by converting it into a system of differential of the order one. Theoretical considerations has been discussed and some examples were presented to show the ability of the method for linear and nonlinear systems of differential equations. We use MAPLE computer algebra systems for numerical calculations [G. Frank, MAPLE V, CRC Press Inc., Florida, 1996]. [Copyright &y& Elsevier]

In [Appl. Math. Comput. 140 (2003) 77] and [Appl. Math. Comput., in press] a reducing and modified reducing index methods have been proposed for some cases of semi-explicit DAEs (differential-algebraic equations). In this paper, these methods are generalized to more cases. Also, numerical implementation of generalized methods will be presented through pseudospectral method with domain decomposition. In addition, aforementioned methods will be considered by some examples. [Copyright &y& Elsevier]

In this paper, numerical solution of differential–algebraic equations (DAEs) with index-2 is considered. An index reduction for DAE with index-2 is suggested. First index-2 system is reduced to index-1 system. Then we have applied the method for solving DAEs with index-2 numerically. [Copyright &y& Elsevier]