http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/581383.htmlSeveral software reliability growth models (SRGMs) have been developed by software developers in tracking and measuring the growth of reliability. As the size of software system is large and the number of faults detected during the testing phase becomes large, so the change of the number of faults that are detected and removed through each debugging becomes sufficiently small compared with the initial fault content at the beginning of the testing phase. In such a situation, we can model the software fault detection process as a stochastic process with continuous state space. In this paper, we propose a new software reliability growth model based on Itô type of stochastic differential equation. We consider an SDE-based generalized Erlang model with logistic error detection function. The model is estimated and validated on real-life data sets cited in literature to show its flexibility. The proposed model integrated with the concept of stochastic differential equation performs comparatively better than the existing NHPP-based models.P. K. Kapur, Sameer Anand, Shigeru Yamada, and Venkata S. S. Yadavalli© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/164303.htmlWe study the initial boundary value problem of the nonlinear Klein-Gordon equation. First we introduce a family of potential wells. By using them, we obtain a new existence theorem of global solutions and show the blow-up in finite time of solutions. Especially the relation between the above two phenomena is derived as a sharp condition.Zhao Junsheng and Li Shufeng© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/243290.htmlTwo nonlinear conjugate gradient-type methods for solving unconstrained optimization problems are proposed. An attractive property of the methods, is that, without any line search, the generated directions always descend. Under some mild conditions, global convergence results for both methods are established. Preliminary numerical results show that these proposed methods are promising, and competitive with the well-known PRP method.Jianguo Zhang, Yunhai Xiao, and Zengxin Wei© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/234849.htmlThis paper outlines a detailed study of some relatively new techniques which are originated by He for solving diversified nonlinear problems of physical nature. In particular, we will focus on the variational iteration method (VIM) and its modifications, the homotopy perturbation method (HPM), the parameter expansion method, and exp-function method. These relatively new but very reliable techniques proved useful for solving a wide class of nonlinear problems and are capable to cope with the versatility of the physical problems. Several examples are given to reconfirm the efficiency of these algorithms. Some open problems are also suggested for future research work.Syed Tauseef Mohyud-Din, Muhammad Aslam Noor, and Khalida Inayat Noor© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/207971.htmlOver the last couple of decades, many methods for synchronizing chaotic systems have been proposed with communications applications in view. Yet their performance has proved disappointing in face of the nonideal character of usual channels linking transmitter and receiver, that is, due to both noise and signal propagation distortion. Here we consider a discrete-time master-slave system that synchronizes despite channel bandwidth limitations and an allied communication system. Synchronization is achieved introducing a digital filter that limits the spectral content of the feedback loop responsible for producing the transmitted signal.Marcio Eisencraft, Renato D. Fanganiello, and Luiz A. Baccala© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/378614.htmlWe introduce fractional order into an HIV model. We consider the effect of viral diversity on the human immune system with frequency dependent rate of proliferation of cytotoxic T-lymphocytes (CTLs) and rate of elimination of infected cells by CTLs, based on a fractional-order differential equation model. For the one-virus model, our analysis shows that the interior equilibrium which is unstable in the classical integer-order model can become asymptotically stable in our fractional-order model and numerical simulations confirm this. We also present simulation results of the chaotic behaviors produced from the fractional-order HIV model with viral diversity by using an Adams-type predictor-corrector method.Haiping Ye and Yongsheng Ding© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/510934.htmlThe inverse problem of using measurements to estimate unknown parameters of a system often arises in engineering practice and scientific research. This paper proposes a Collage-based parameter inversion framework for a class of partial differential equations. The Collage method is used to convert the parameter estimation inverse problem into a minimization problem of a function of several variables after the partial differential equation is approximated by a differential dynamical system. Then numerical schemes for solving this minimization problem are proposed, including grid approximation and ant colony optimization. The proposed schemes are applied to a parameter estimation problem for the Belousov-Zhabotinskii equation, and the results show that the proposed approximation method is efficient for both linear and nonlinear partial differential equations with respect to unknown parameters. At worst, the presented method provides an excellent starting point for traditional inversion methods that must first select a good starting point.Xiaoyan Deng and Qingxi Liao© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/495360.htmlThe paper presents a new algorithm for determination of pulse edges of a modulated wave of a PWM voltage inverter which offers a possibility that natural sampling is realized with an arbitrary accuracy without applying an iterative procedure. The basic idea is to express the angles which determine pulse edges of the modulated signal as polynomials of amplitude modulation index. Geometric interpretation of sampling of the polynomial algorithm is identical with the geometric interpretation of natural algorithm, but the transcendental equation whose solution defines pulse edges of the modulated signal is replaced by a simple procedure of finding values of a polynomial whose coefficients are determined in advance by an exact procedure. This approach gives the possibility of digital implementation of polynomial sampling method using the low-cost microprocessor platforms.Dragutin Kostić and Vladimir Šinik© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/946245.htmlWe study the dynamical behavior of a single inductor two inputs two outputs (SITITO) power electronics DC-DC converter under a current mode control in a PWM interleaved scheme. This system is able to regulate two, generally one positive and one negative, voltages (outputs). The regulation of the outputs is carried out by the modulation of two time intervals within a switching cycle. The value of the regulated voltages is related to both duty cycles (inputs). The stability of the whole nonlinear system is therefore studied without any decoupling. Under certain operating conditions, the dynamical behavior of the system can be modeled by a piecewise linear (PWL) map, which is used to investigate the stability in the parameter space and to detect possible subharmonic oscillations and chaotic behavior. These results are confirmed by numerical one dimensional and two-dimensional bifurcation diagrams and some experimental measurements from a laboratory prototype.Abdelali El Aroudi, Vanessa Moreno-Font, and Luis Benadero© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/358329.htmlWe characterize well-posedness in Hölder spaces for an abstract version of the equation (∗) u′′+λu′′′=c2(Δu+μΔu′)+f which model the vibrations of flexible structures possessing internal material damping and external force f. As a consequence, we show that in case of the Laplacian with Dirichlet boundary conditions, equation (∗) is always well-posed provided 0<λ<μ.Claudio Cuevas and Carlos Lizama© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/902506.htmlLet UF be the Floquet operator of a time periodic Hamiltonian H(t). For each positive and discrete observable A (which we call a probe energy), we derive a formula for the Laplace time average of its expectation value up to time T in terms of its eigenvalues and Green functions at the circle of radius e1/T. Some simple applications are provided which support its usefulness.César R. de Oliveira and Mariza S. Simsen© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/975901.htmlLet ℍn be the Heisenberg group. The fundamental manifold of the radial function space for ℍn can be denoted by [0,+∞)×ℝ, which is just the Laguerre hypergroup. In this paper the multiresolution analysis on the Laguerre hypergroup 𝕂=[0,+∞)×ℝ is defined. Moreover the properties of Haar wavelet bases for La2(𝕂) are investigated.Peizhu Xie and Jianxun He© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/935030.htmlHirota's bilinear form for the Complex Modified Korteweg-de Vries-II equation (CMKdV-II) Ut−6|U|2Ux+Uxxx=0 is derived. We obtain one- and two-soliton solutions analytically for the CMKdV-II. One-soliton solution of the CMKdV-II equation is obtained by using finite difference method by implementing an iterative method.Ömer Akin and Ersin Özuğurlu© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/372703.htmlThe purpose of this article is to develop and validate a computational method for the solution of viscous incompressible flow in a domain with specified static or total pressure on the flow-through boundaries (inflow and outflow). The computational algorithm is based on the Finite Volume Method in nonstaggered boundary-fitted grid. The implementations of the boundary conditions on the flow-through parts of the boundary are discussed. Test examples illustrate the main features and validity of the proposed method to study viscous incompressible flow through a bounded domain with specified static pressure (or total pressure) on boundary as a part of well-posed boundary conditions.N. P. Moshkin and D. Yambangwai© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/249361.htmlWe employ the bifurcation theory of planar dynamical systems to investigate the exact travelling wave solutions of a generalized Degasperis-Procesi equation ut−uxxt+4uux+γ(u−uxx)x=3uxuxx+uuxxx. The implicit expression of smooth soliton solutions is given. The explicit expressions of peaked soliton solutions and periodic cuspon solutions are also obtained. Further, we show the relationship among the smooth soliton solutions, the peaked soliton solutions, and the periodic cuspon solutions. The physical relevance of the found solutions and the reason why these solutions can exist in this equation are also given.Jiangbo Zhou and Lixin Tian© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/394387.htmlThe higher period stochastic bifurcation of a nonlinear airfoil fluid-structure interaction system is analyzed using an efficient and robust uncertainty quantification method for unsteady problems. The computationally efficient numerical approach achieves a constant error with a constant number of samples in time. The robustness of the method is assured by the extrema diminishing concept in probability space. The numerical results demonstrate that the system is even more sensitive to randomness at the higher period bifurcation than in the first bifurcation point. In this isolated point in parameter space the clear hierarchy of increasing importance of the random nonlinearity parameter, initial condition, and natural frequency ratio, respectively, even suddenly reverses. Disregarding seemingly less important random parameters based on a preliminary analysis can, therefore, be an unreliable approach for reducing the number of relevant random input parameters.Jeroen A. S. Witteveen and Hester Bijl© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/969610.htmlWe use an unconditionally stable parallel difference scheme to solve telegraph equation. This method is based on domain decomposition concept and using asymmetric Saul'yev schemes for internal nodes of each sub-domain and alternating group implicit method for sub-domain's interfacial nodes. This new method has several advantages such as: good parallelism, unconditional stability and better accuracy than original Saul'yev schemes. The details of implementation and proving stability are briefly discussed. Numerical experiments on stability and accuracy are also presented.A. Borhanifar and Reza Abazari© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/603916.htmlAn analysis has been performed to study magneto-hydrodynamic (MHD) squeeze flow between two parallel infinite disks where one disk is impermeable and the other is porous with either suction or injection of the fluid. We investigate the combined effect of inertia, electromagnetic forces, and suction or injection. With the introduction of a similarity transformation, the continuity and momentum equations governing the squeeze flow are reduced to a single, nonlinear, ordinary differential equation. An approximate solution of the equation subject to the appropriate boundary conditions is derived using the homotopy perturbation method (HPM) and compared with the direct numerical solution (NS). Results showing the effect of squeeze Reynolds number, Hartmann number and the suction/injection parameter on the axial and radial velocity distributions are presented and discussed. The approximate solution is found to be highly accurate for the ranges of parameters investigated. Because of its simplicity, versatility and high accuracy, the method can be applied to study linear and nonlinear boundary value problems arising in other engineering applications.G. Domairry and A. Aziz© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/282307.htmlFor block-tridiagonal linear system of equations, a variant of tangential filtering preconditioners is proposed in this paper. The new variant is based on a twisted block factorization along with certain filtering property. For practical usage, a class of composite preconditioners tested, which are constructed by combining the twisted tangential filtering decomposition preconditioner with the classical ILU(0) preconditioner in a multiplicative way. The performance of the new preconditioners is compared with other classical preconditioners; the superiority and the weakness of the preconditioners are pointed out.Ruirui Wang, Qiang Niu, and Linzhang Lu© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/575131.htmlThis paper presents a positional FEM formulation to deal with geometrical nonlinear dynamics of shells. The main objective is to develop a new FEM methodology based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors not displacements and rotations. These characteristics are the novelty of the present work and avoid the use of large rotation approximations. A nondimensional auxiliary coordinate system is created, and the change of configuration function is written following two independent mappings from which the strain energy function is derived. This methodology is called positional and, as far as the authors' knowledge goes, is a new procedure to approximated geometrical nonlinear structures. In this paper a proof for the linear and angular momentum conservation property of the Newmark β algorithm is provided for total Lagrangian description. The proposed shell element is locking free for elastic stress-strain relations due to the presence of linear strain variation along the shell thickness. The curved, high-order element together with an implicit procedure to solve nonlinear equations guarantees precision in calculations. The momentum conserving, the locking free behavior, and the frame invariance of the adopted mapping are numerically confirmed by examples.Humberto Breves Coda and Rodrigo Ribeiro Paccola© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/256765.htmlSynchronization plays an important role in telecommunication systems, integrated circuits, and automation systems. Formerly, the masterslave synchronization strategy was used in the great majority of cases due to its reliability and simplicity. Recently, with the wireless networks development, and with the increase of the operation frequency of integrated circuits, the decentralized clock distribution strategies are gaining importance. Consequently, fully connected clock distribution systems with nodes composed of phase-locked loops (PLLs) appear as a convenient engineering solution. In this work, the stability of the synchronous state of these networks is studied in two relevant situations: when the node filters are first-order lag-lead low-pass or when the node filters are second-order low-pass. For first- order filters, the synchronous state of the network shows to be stable for any number of nodes. For second-order filter, there is a superior limit for the number of nodes, depending on the PLL parameters.Átila Madureira Bueno, André Alves Ferreira, and José Roberto C. Piqueira© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/104547.htmlContinuation is an efficient algorithm for finding solutions of systems of nonlinear algebraic equations where the solutions form a one-dimensional continuum. Such systems arise naturally when investigating equilibrium points and periodic solutions of ordinary differential equations with one parameter. Continuation of isolated periodic solutions of dissipative systems is a well-established technique. Less attention has been devoted to continuation of periodic solutions of conservative systems, where periodic solutions typically form a one-parameter family. To specify a single periodic solution, additional condition must be considered. However, this gives an over-determined system, which has no solution when working with approximate numerical values. We propose a simple algorithm which solves this difficulty by using singular value decomposition of the Jacobian matrix. This algorithm is applied to the conservative model of elastic pendulum. A branch of periodic solutions with constant energy is found which is born by the period doubling bifurcation of vertical oscillations.P. Pokorny© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/610574.htmlThe coupled system of two forced Liénard-type oscillators has applications in diode-based electric circuits and phenomenological models for the heartbeat. These systems typically exhibit intermittent transitions between laminar and chaotic states; what affects their performance and, since noise is always present in such systems, dynamical models should include these effects. Accordingly, we investigated numerically the effect of noise in two intermittent phenomena: the intermittent transition to synchronized behavior for identical and unidirectionally coupled oscillators, and the intermittent transition to chaos near a periodic window of bidirectionally coupled oscillators. We found that the transition from a nonsynchronized to a synchronized state exhibits a power-law scaling with exponent 3/2 characterizing on-off intermittency. The inclusion of noise adds an exponential tail to this scaling.Ângela Maria dos Santos, Sérgio Roberto Lopes, and Ricardo Luiz Viana© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/238960.htmlThis paper reviews the major developments of modeling techniques applied to nonlinear dynamics and chaos. Model representations, parameter estimation techniques, data requirements, and model validation are some of the key topics that are covered in this paper, which surveys slightly over two decades since the pioneering papers on the subject appeared in the literature.Luis A. Aguirre and Christophe Letellier© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/507815.htmlNew travelling wave solutions to the Fornberg-Whitham equation ut−uxxt+ux+uux=uuxxx+3uxuxx are investigated. They are characterized by two parameters. The expresssions for the periodic and solitary wave solutions are obtained.Jiangbo Zhou and Lixin Tian© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/368024.htmlThe unit commitment (UC) problem which is an important subject in power system engineering is solved by using Lagragian relaxation (LR), penalty function (PF), and augmented Lagrangian penalty function (ALPF) methods due to their higher solution quality and faster computational time than metaheuristic approaches. This problem is considered to be a nonlinear programming-(NP-) hard problem because it is nonlinear, mixed-integer, and nonconvex. These three methods used for solving the problem are based on dual optimization techniques. ALPF method which combines the algorithmic aspects of both LR and PF methods is firstly used for solving the UC problem. These methods are compared to each other based on feasible schedule for each stage, feasible cost, dual cost, duality gap, duration time, and number of iterations. The numerical results show that the ALPF method gives the best duality gap, feasible and dual cost instead of worse duration time and the number of iterations. The four-unit Tuncbilek thermal plant which is located in Kutahya region in Turkey is chosen as a test system in this study. The programs used for all the analyses are coded and implemented using general algebraic modeling system (GAMS).Mehmet Kurban and Ümmühan Başaran Filik© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/678519.htmlLet E be a real uniformly convex Banach space, and let{Ti:i∈I} be N nonexpansive mappings from E into itself with F={x∈E:Tix=x, i∈I}≠ϕ, where I={1,2,…,N}. From an arbitrary initial point x1∈E, hybrid iteration scheme {xn} is defined as follows: xn+1=αnxn+(1−αn)(Tnxn−λn+1μA(Tnxn)), n≥1, where A:E→E is an L-Lipschitzian mapping, Tn=Ti, i=n(mod N), 1≤i≤N, μ>0, {λn}⊂[0,1), and {αn}⊂[a,b] for some a,b∈(0,1). Under some suitable conditions, the strong and weak convergence theorems of {xn} to a common fixed point of the mappings {Ti:i∈I} are obtained. The results presented in this paper extend and improve the results of Wang (2007) and partially improve the results of Osilike, Isiogugu, and Nwokoro (2007).Lin Wang, Yi-Juan Chen, and Rong-Chuan Du© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/948672.htmlThe main object of this paper is to study the weakly nonlinear hydrodynamic stability of the thin Newtonian fluid flowing on a rotating circular disk. A long-wave perturbation method is used to derive the nonlinear evolution equation for the film flow. The linear behaviors of the spreading wave are investigated by normal mode approach, and its weakly nonlinear behaviors are explored by the method of multiple scales. The Ginzburg-Landau equation is determined to discuss the necessary condition for the existence of such flow pattern. The results indicate that the superctitical instability region increases, and the subcritical stability region decreases with the increase of the rotation number or the radius of circular disk. It is found that the rotation number and the radius of circular disk not only play the significant roles in destabilizing the flow in the linear stability analysis but also shrink the area of supercritical stability region at high Reynolds number in the weakly nonlinear stability analysis.Cha'o-Kuang Chen and Ming-Che Lin© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/728105.htmlWe present control strategies of a diffusion process for chemical vapor deposition for metallic bipolar plates. In the models, we discuss the application of different models to simulate the plasma-transport of chemical reactants in the gas-chamber. The contribution are an optimal control problem based on a PID control to obtain a homogeneous layering. We have taken into account one- and two-dimensional problems that are given with constraints and control functions. A finite-element formulation with adaptive feedback control for time-step selection has been developed for the diffusion process. The optimization is presented with efficient algorithms. Numerical experiments are discussed with respect to the diffusion processes of the macroscopic model.Jürgen Geiser and Christian Fleck© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/mpe/2009/728916.htmlTrain scheduling has been a significant issue in the railway industry. Over the last few years, numerous approaches and tools have been developed to compute railway scheduling. In this paper, we present a set of heuristics for a constraint-based train scheduling tool, which is a project in collaboration with the National Network of Spanish Railways (RENFE), Spain. We formulate train scheduling as constraint optimization problems. Three heuristics are developed to speed up and direct the search toward suboptimal solutions in periodic train scheduling problems. The feasibility of our problem-oriented heuristics is confirmed with experimentation using real-life data. The results show that these techniques enable MIP solvers such as LINGO and ILOG Concert Technology (CPLEX) to terminate earlier with good solutions.Miguel A. Salido and Federico Barber© 2009, Hindawi Publishing Corporation. All rights reserved.