A recent survey on computational techniques for solving singularly perturbed boundary value problems

This survey paper contains a surprisingly large amount of material and indeed can serve as an introduction to some of ideas and methods of singular perturbation theory. In continuation of a survey performed earlier, this paper limits its coverage to some standard numerical methods developed by numerous researchers between 2000 and 2005. A summary of the results of some recent methods is presented and this leads to conclusions and recommendations regarding methods to use on singular perturbation problems. Because of space constraints, we considered one-dimensional singularly perturbed boundary value problems only.     

On an inexact Uzawa-type algorithm for stabilized saddle point problems

In this article, we study the convergence of an inexact Uzawa-type algorithm for solving stabilized saddle point problems. It is shown that for stabilized problems, the algorithm converges under the same condition as that in classical case.     

A higher order method for multiple zeros of nonlinear functions

A method of order three for finding multiple zeros of nonlinear functions is developed. The method requires two evaluations of the function and one evaluation of the derivative per step.     

Dynamics of a fifth-order iterative method

In this paper, we study the dynamical behaviour of a two-point iterative method with order of convergence five to solve nonlinear equations in the complex plane. In fact, we complement the dynamical study started in previous works with a more systematic analysis for polynomials with at most two different roots and different multiplicities. In addition, we characterize some polynomials of degree greater or equal to 4, such that the related methods are not generally convergent. We also analyse the degrees of the rational functions associated with two-point methods when they are applied to polynomials of degree n, showing their dependence on n ² and how this fact considerably complicates the dynamical study.     

Internal preference mapping and the issue of satiety

Internal preference mapping (IPM) and Landscape Segmentation Analysis® (LSA) are two techniques broadly used to unfold consumers’ overall product liking ratings and create spatial maps that will provide further insights on consumers’ preferences. IPM is based on a vector model while LSA involves an ideal point model. Through a simulation and the analysis of 27 market research data sets, it is shown that IPM consistently creates a hedonic dimension that prevents the identification of satiety prone attributes (intensities higher or lower than a optimal level being disliked by the consumers) on that dimension. As a result, subsequent steps taken upon generating an IPM map such as the investigation of drivers of liking, population segmentation and the estimation of optimal product profiles have also a strong likelihood of resulting in distorted results, the level of distortion being dependent on the actual configuration of the underlying structure that IPM tried to uncover. It is also shown that a technique based on ideal points such as LSA does not exhibit this systematic artifact when unfolding liking data. Consequently, sensory scientists and market researchers should use caution when interpreting and using results issued from an internal preference mapping analysis.     

A triparametric family of three-step optimal eighth-order methods for solving nonlinear equations

A new triparametric family of three-step optimal eighth-order iterative methods free from second derivatives are proposed in this paper, to find a simple root of nonlinear equations. Convergence analysis as well as numerical experiments confirms the eighth-order convergence and asymptotic error constants.     

Numerical treatment of a quasilinear initial value problem with boundary layer

The paper deals with the singularly perturbed quasilinear initial value problem exhibiting initial layer. First the nature of solution of differential problem before presenting method for its numerical solution is discussed. The numerical solution of the problem is performed with the use of a finite-fitted difference scheme on an appropriate piecewise uniform mesh (Shishkin-type mesh). An error analysis shows that the method is first-order convergent except for a logarithmic factor, in the discrete maximum norm, independently of the perturbation parameter. Finally, numerical results supporting the theory are presented.     

朱光潜青年教育思想探析

美学大师朱光潜也是一位对青年教育倾注热忱的教育学家。"尽人之性,培养‘全人’""德育为首,学会做人""怡情养性,美化人生""引路启发,催生潜能"是朱先生青年教育思想的四个主要方面,这些教育思想迄今仍具有重要的借鉴意义。     

均值模型下满足对数级收敛速度的动态系统

文章研究了在均值模型下,动态系统收敛至一致性状态所需的时间。在每一时间步内,节点计算其邻居的均值,并以计算结果作为自己的新值。我们考虑了当节点间的网络结构处于动态变化状态的情况。我们的分析证明了当节点的度在相邻时间点之间变化较小的情况下,即使仅满足微弱的连通性条件,动态变化的网络仍然可以保证动态系统会快速收敛到一致性状态。     

Disturbance observer based hierarchical control of coaxial-rotor UAV

This paper propose an hierarchical controller based on a new disturbance observer with finite time convergence (FTDO) to solve the path tracking of a small coaxial-rotor-typs Unmanned Aerial Vehicles (UAVs) despite of unknown aerodynamic efforts. The hierarchical control technique is used to separate the flight control problem into an inner loop that controls attitude and an outer loop that controls the thrust force acting on the vehicle. The new disturbance observer with finite time convergence is intergated to online estimate the unknown uncertainties and disturbances and to actively compensate them in finite time.The analysis further extends to the design of a control law that takes the disturbance estimation procedure into account. Numerical simulations are carried out to demonstrate the efficiency of the proposed control strategy.