对流扩散方程的三层WENO-MMOCAA差分方法

本文把三层修正特征线法,MMOCAA 差分方法及WENO 插值相结合,提出了求解对流扩散方程的三层WENO-MMOCAA 差分格式.此格式关于时间具有二阶精度,关于空间具有二阶以上精度且可避免基于二次以上Lagrange 插值的三层MMOCAA 差分方法在解的大梯度附近所产生的振荡.本文使用新的分析方法,给出了格式的误差估计.本文的数值算例表明新格式可消除振荡.     

求解对流扩散方程的低耗散中心迎风格式

以四阶CWENO重构为基础,通过将对流项采用低耗散中心迎风格式离散,扩散项采用四阶中心差分格式离散,对得到的半离散格式采用四阶龙格库塔方法在时间方向上推进,得到一种求解对流扩散方程的高阶有限差分格式.数值结果验证了该格式的四阶精度和基本无振荡特性.     

对流扩散方程的本质非振荡特征差分方法

本文把特征差分法[1]和本质非振荡插值[3]相结合,提出了对流扩散方程的本质非荡性征差分格式,避免了基于Lagrange插值特征差分格式在求解解具有大梯度问题时所产生的非物理振荡,并给出了格式的严格误差估计及数值算例。     

变系数双侧空间回火分数阶对流-扩散方程的隐式中点法

针对带非线性源项的变系数双侧空间回火分数阶对流-扩散方程,采用隐式中点法离散一阶时间偏导数,中心差商公式离散对流项,用二阶回火加权移位差分算子逼近左、右Riemann-Liouville空间回火分数阶偏导数,构造了一类新的数值格式.证明了数值方法的稳定性和收敛性,且方法在时间和空间均为二阶收敛.数值试验验证了数值方法的理论分析结果.     

对流扩散方程的三层ENO-MMOCAA差分方法

本文把多步修正特征线法[1],MMOCAA差分方法[2]及ENO插值[3]相结合,提出了求解对流扩散方程的多步ENO-MMOCAA差分方法.该方法关于时间及空间都具有二阶以上的精度且可避免在解的大梯度附近产生振荡.本文给出了格式的误差估计及数值算例.     

一种求解运动曲面上对流扩散方程的三维水平集方法

给出了一种求解运动曲面上对流扩散方程的三维水平集算法. 水平集函数被用来表示曲面.曲面上的微分方程及其解通过水平集方法被延拓到包含曲面的一个小邻域中. 一种半隐式的Crank-Nicholson 格式被用来做时间推进, 中心差分和三阶加权实质无振荡(WENO) 格式被分别用来离散方程中的扩散项和对流项. 分析证明了它在标准的Courant-Friedrichs-Lewy (CFL) 条件下的稳定性. 数值算例显示了它能取得二阶精度.     

多项式基函数法

提出一种新型的数值计算方法--基函数法.此方法直接在非结构网格上离散微分算子,采用基函数展开逼近真实函数,构造出了导数的中心格式和迎风格式,取二阶多项式为基函数,并采用通量分裂法及中心格式和迎风格式相结合的技术以消除激波附近的非物理波动,构造出数值求解无粘可压缩流动二阶多项式的基函数格式,通过多个二维无粘超音速和跨音速可压缩流动典型算例的数值计算表明,该方法是一种高精度的、对激波具有高分辨率的无波动新型数值计算方法,与网格自适应技术相结合可得到十分满意的结果.     

带非线性源项的Riesz回火分数阶扩散方程的预估校正方法

本文针对带非线性源项的Riesz回火分数阶扩散方程,利用预估校正方法离散时间偏导数,并用修正的二阶Lubich回火差分算子逼近Riesz空间回火的分数阶偏导数,构造出一类新的数值格式.给出了数值格式在一定条件下的稳定性与收敛性分析,且该格式的时间与空间收敛阶均为二阶.数值试验表明数值方法是有效的.     

对流扩散方程的高效稳定差分格式

基于二阶修正Dennis格式 ,提出了采用时间相关法求解定常对流扩散方程的一种具有节省内存空间和提高定常解收敛速度的有理式型优化半隐和松驰半隐紧致格式 .本文建立的差分格式具有运算量小、无网格雷诺数限制的优点 ,是无条件稳定和无条件单调的。通过对非线性Burgers方程进行的数值计算结果表明 ,文中构造的有理式型优化半隐和松驰半隐紧致格式适合于非线性问题计算 ,且保持了无条件稳定和无条件单调的特性 ,尤其能使定常解收敛速度加快 ,精度提高 .     

一维对流扩散方程非均匀网格上的指数型高阶紧致差分格式

基于非均匀网格上函数的泰勒级数展开,结合残参量修正法,推导了非均匀网格上对流扩散方程的高阶指数型紧致差分格式,选取的算例表明,格式兼有高精度和高分辨率的优点,能够很好的适用于大梯度变化,计算区域中含边界层和对流占优区域中的流动问题的求解.     

Modified Defect Correction Algorithms for ODEs. Part I: General Theory

The well-known method of Iterated Defect Correction (IDeC) is based on the following idea: Compute a simple, basic approximation and form its defect w.r.t. the given ODE via a piecewise interpolant. This defect is used to define an auxiliary, neighboring problem whose exact solution is known. Solving the neighboring problem with the basic discretization scheme yields a global error estimate. This can be used to construct an improved approximation, and the procedure can be iterated. The fixed point of such an iterative process corresponds to a certain collocation solution. We present a variety of modifications to this algorithm. Some of these have been proposed only recently, and together they form a family of iterative techniques, each with its particular advantages. These modifications are based on techniques like defect quadrature (IQDeC), defect interpolation (IPDeC), and combinations thereof. We investigate the convergence on locally equidistant and nonequidistant grids and show how superconvergent approximations can be obtained. Numerical examples illustrate our considerations. The application to stiff initial value problems will be discussed in Part II of this paper.     

Simple linear approximations to the likelihood equation for combining evidence in multiple 2×2 tables: A critique of conventional procedures

Summary The conventional procedures for a common odds ratio in multiple 2×2 tables are explored and critiqued. Three types of linear approximation to the likelihood equations under some models of common measures of association are used to derive the popular conventional estimators and test statistics. Some of them are derived using the model of the common standardized difference which is an unacceptable measure. The derivation provides us with some characteristics of the procedures. The advantages of procedures based on the conditional and unconditional likelihoods are discussed. The Institute of Statistical Mathematics     

A Quasisteady Stefan Problem with Curvature Correction and Kinetic Undercooling

A quasisteady Stefan problem with curvature correction and kinetic undercooling is considered. It is a problem with phase transition, in which not only the Stefan condition, but also the curvature correction and kinetic undercooling effect hold on the free boundary, and in phase regions elliptic equations are satisfied by the unknown temperature at each time. The existence and uniqueness of a local classical solution of this problem are obtained.     

非光滑第二类Fredholm方程Collocation解的迭代──校正方法

本文对于一类具非光滑核第二类Ｆｒｅｄｈｏｌｍ方程的Ｃｏｌｌｏｃａｔｉｏｎ解提出一种迭代─校正方法，使得在计算量增加很少的前提下，成倍提高逼近解精度，并将此方法用于平面多角域上边界积分方程，从而给出其相应微分方程逼近解的高精度算法。此方法还是一种自适应方法。     

Multivariate density estimation using dimension reducing information and tail flattening transformations

We propose a nonparametric multiplicative bias corrected transformation estimator designed for heavy tailed data. The multiplicative correction is based on prior knowledge and has a dimension reducing effect at the same time as the original dimension of the estimation problem is retained. Adding a tail flattening transformation improves the estimation significantly-particularly in the tail-and provides significant graphical advantages by allowing the density estimation to be visualized in a simple way. The combined method is demonstrated on a fire insurance data set and in a data-driven simulation study.     

HIGH ACCURACY ANALYSIS FORINTEGRODIFFERENTIAL EQUATIONS

1.IntroductionLetfibearectangulardomain.WeconsidertheRichardsonextrapolationanddefectcorrectionofthefiniteelementapproximationstothesolutionsofthefollowingsimpleparabolicintegrodifferentialequationsItiswellknownthattheextrapolationmethodsareveryeffectivenumericalmethodsinproducinghigheraccuracyapproximations.Thistechniqueusedforthefiniteelemelltapproximationstothesolutionsofellipticdifferentialequationshasbeenwelldemonstratedin[l--3,5--7,14--18,22and24].Andthistechniquehasalsobeenconsideredfo…     

A HIGH ORDER METHOD FOR NON-SMOOTH FREDHOLM EQUATIONS

1.IntroductionConsidertheequationwherek(s,t)=k(f)tandf(s)aregiven,uistheunknownsolution.SinceitisrelatedcloselytoWiener-Hopfequationsandisveryimportantinpractice,therearemanynumericalresultsaboutit(e.g.[1--11]).Itiswellknownthattheaccuracyoftheapproximati…     

Modified defect correction algorithms for ODEs. Part II: Stiff initial value problems

As shown in part I of this paper and references therein, the classical method of Iterated Defect Correction (IDeC) can be modified in several nontrivial ways, extending the flexibility and range of applications of this approach. The essential point is an adequate definition of the defect, resulting in a significantly more robust convergence behavior of the IDeC iteration, in particular, for nonequidistant grids. The present part II is devoted to the efficient high-order integration of stiff initial value problems. By means of model problem investigation and systematic numerical experiments with a set of stiff test problems, our new versions of defect correction are systematically evaluated, and further algorithmic measures are proposed for the stiff case. The performance of the different variants under consideration is compared, and it is shown how strong coupling between non-stiff and stiff components can be successfully handled. AMS subject classification 65L05 Supported by the Austrian Research Fund (FWF) grant P-15030.     

EXTRAPOLATION AND DEFECT CORRECTION FOR DIFFUSION EQUATIONS WITH BOUNDARY INTEGRAL CONDITIONS

1IntroductionIn[8],we11avestudiedparabolicintegrodifferentialequationswithhomogeneousboundaryconditionsbyextrapolatiollandcorrectionmethods,andderivedGalerkinapproximationsofthirdorder.Nowweturntodiffusionequationswithboundaryintegralconditions.Letfibearectangulardomain.Weareconcernedwitlltheapproximationtothesolutionofthemodelproblemwheren(x,y)=(m(x,y),"Z(x,y))istheouter--normaldirectiononoff.2GlobalExtrapolationFirstofall,wediscussextrpolationfortheproblem(1.l).Throughouttilepaper,weassum…     

A construction of pooling designs with surprisingly high degree of error correction

It is well known that many famous pooling designs are constructed from mathematical structures by the “containment matrix” method. In this paper, we propose another method and obtain a family of pooling designs with surprisingly high degree of error correction based on a finite set. Given the numbers of items and pools, the error-tolerant property of our designs is much better than that of Macula?s designs when the size of the set is large enough.