A modified predictor–corrector scheme for the two-dimensional sine-Gordon equation

A three-time level finite-difference scheme based on a fourth order in time and second order in space approximation has been proposed for the numerical solution of the nonlinear two-dimensional sine-Gordon equation. The method, which is analysed for local truncation error and stability, leads to the solution of a nonlinear system. To avoid solving it, a predictor–corrector scheme using as predictor a second-order explicit scheme is proposed. The procedure of the corrector has been modified by considering as known the already evaluated corrected values instead of the predictor ones. This modified scheme has been tested on the line and circular ring soliton and the numerical experiments have proved that there is an improvement in the accuracy over the standard predictor–corrector implementation. This research was co-funded by E.U. (75%) and by the Greek Government (25%).     

Instabilities in the Chapman-Enskog Expansion and Hyperbolic Burnett Equations

It is well-known that the classical Chapman-Enskog procedure does not work at the level of Burnett equations (the next step after the Navier-Stokes equations). Roughly speaking, the reason is that the solutions of higher equations of hydrodynamics (Burnett's, etc.) become unstable with respect to short-wave perturbations. This problem was recently attacked by several authors who proposed different ways to deal with it. We present in this paper one of possible alternatives. First we deduce a criterion for hyperbolicity of Burnett equations for the general molecular model and show that this criterion is not fulfilled in most typical cases. Then we discuss in more detail the problem of truncation of the Chapman-Enskog expansion and show that the way of truncation is not unique. The general idea of changes of coordinates (based on analogy with the theory of dynamical systems) leads finally to nonlinear Hyperbolic Burnett Equations (HBEs) without using any information beyond the classical Burnett equations. It is proved that HBEs satisfy the linearized H-theorem. The linear version of the problem is studied in more detail, the complete Chapman-Enskog expansion is given for the linear case. A simplified proof of the Slemrod identity for Burnett coefficients is also given.     

两种拔尿管方法对膀胱功能损伤的临床观察

为观察两种不同的拔尿管方法对膀胱功能损伤的差异,将80例患者随机分成两组,分别采用改良法(40例)和常规法(40例)拔除留置尿管,分析比较了两组患者排尿顺利率、逼尿肌功能恢复率及尿道刺激症、尿失禁、尿潴留。结果表明,两组患者拔管后上述指标与情况有显著性差异,P<0.05。提示改良组膀胱功能损伤明显低于对照组。改良的拔管方法是一种值得护理推广应用的好方法。     

Multilevel preconditioners for a quadrature Galerkin solution of a biharmonic problem

Efficient multilevel preconditioners are developed and analyzed for the quadrature finite element Galerkin approximation of the biharmonic Dirichlet problem. The quadrature scheme is formulated using the Bogner–Fox–Schmit rectangular element and the product two‐point Gaussian quadrature. The proposed additive and multiplicative preconditioners are uniformly spectrally equivalent to the operator of the quadrature scheme. The preconditioners are implemented by optimal algorithms, and they are used to accelerate convergence of the preconditioned conjugate gradient method. Numerical results are presented demonstrating efficiency of the preconditioners. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006     

Adaptive Algorithm for Constrained Least-Squares Problems

This paper is concerned with the implementation and testing of an algorithm for solving constrained least-squares problems. The algorithm is an adaptation to the least-squares case of sequential quadratic programming (SQP) trust-region methods for solving general constrained optimization problems. At each iteration, our local quadratic subproblem includes the use of the Gauss–Newton approximation but also encompasses a structured secant approximation along with tests of when to use this approximation. This method has been tested on a selection of standard problems. The results indicate that, for least-squares problems, the approach taken here is a viable alternative to standard general optimization methods such as the Byrd–Omojokun trust-region method and the Powell damped BFGS line search method.     

Solution of large‐scale weighted least‐squares problems

A sequence of least‐squares problems of the form min_y∥G^1/2(A^T y?h)∥₂, where G is an n×n positive‐definite diagonal weight matrix, and A an m×n (m?n) sparse matrix with some dense columns; has many applications in linear programming, electrical networks, elliptic boundary value problems, and structural analysis. We suggest low‐rank correction preconditioners for such problems, and a mixed solver (a combination of a direct solver and an iterative solver). The numerical results show that our technique for selecting the low‐rank correction matrix is very effective. Copyright © 2002 John Wiley & Sons, Ltd.     

拆边法求最短路径

本文利用局部比较法 ,在图中定义子图、无效路径、以及可去边 .利用推导的有关定理 ,拆去可去边 ,利用最短路径相同的等价性 ,达到化简图 ,从而求出最短路径     

最速下降规则不失为一可用规则

本从统计意义上平均迭代次数的观点出发，指出求解线性规划的最速下降规则是可取的，好用的。     

关于AOR迭代法的研究

本文论证了严格对角占优矩阵之AOR法的误差估计式中的误差估计常数hγ,ω（0≤γ≤ω0）的最小值是h1,1.     

线性分式规划最优解集的求法

本文使用多面集的表示定理，导出了线性分式规划最优解集的结构，并给出确定全部最优解的计算步骤。