A REMARK ON THE GLOBAL SMALL SOLUTION FOR GENERAL COUPLED MAXWELL-SCHR■DINGER EQUATIONS IN IR~3

1.IntroductionandMainResultInthispaperwecontinuetostudytheCauchyproblemforgeneralcoupledMaxwellmSchrsdingerequations.Whenthespatialdimensionsarethree,weprovetileexistenceofglobalsmallsolutionfortheCauchyproblemofgeneralcoupledMaxwellSchrsdingerequationsunderLorentzgaugebyapplyingthequasi--energymethodwhichwasintroducedbyV.M.n.erieril].Basingon[2]or[3],CauchyproblemforgeneralcoupledMaxwelL'Schri'dingerequationsunderLorentzgaugecanbewrittenaswherex6R",p,urangeover0,112,3,jrangesover112,3a…     

二阶积-微分方程奇异边值问题解的存在性

讨论了一类二阶积 微分方程两点边值问题解的存在性。该问题以四阶微分方程两点边值问题为特例。首先在不假设非线性项单调,并允许其有奇性的情况下,利用上下解方法与Schauder不动点定理,获得了二阶Fredholm型积 微分方程两点边值问题解的存在性结果,然后把该结果应用于两端简单支撑的弹性梁的平衡状态模型—四阶微分方程边值问题。     

THE CAUCHY PROBLEM FOR GENERAL COUPLEDMAXWELL-SCHR■DINGER EQUATIONS (II)

1.IntroductionandMainResultIn{11westudiedthelocalwell-posednessfortheCauchyproblemforgeneralcoupledMaxwelLSchr6dingerequations.Thisisacontinuationof[1].ItisdevotedtothestudyoftheglobalexistenceofCauchyproblemforgeneralcoupledMaxwell--SchrodlugerequaticusunderLorentzgaugewhenthespatialdimensionsareoneortwobyapplyingthequasi-energymethodwhichwasintroducedbyV.Moncerieft2].Basingon[1],theCauchyproblemforgeneralcoupledMaxweif--Schr6dingerequaticusnuderLorentzgaugecanbewrittenaswherexER",p,u…     

ON A PROPERTY OF SOLUTIONS OF M-MATRIXEQUATIONS

1.IntroductionConsideringthefollowingsystemoflinearequationsAx~b(l.1)whereAisannxnM-matrix,bisanndimensionalvectorandbeRang(A).Theresearchonthesolutionofequation(1.1)isveryimportantinLeontiefmodelofinput-outputanalysis(see[1,2]).G.St..k.ma[Zjstudiestheabo…     

SOME STABILITY THEOREMS FOR DIFFERENCE EQUATIONS WITH TIME DELAY

1.IntroductionDifferellceequationswithtimedelayhavebeenanimportantclassofmathematicallllodels.Fol'instance,inbiology,systemsofdifferenceequationshavebeedmuchusedtomodeltheinteractiollsofspecieswithlion-overlappinggeneration,butthemodelwillberelatedtodifferenceequationswithtimedelaywhenollemustconsidertheinfluenceoftimedelayeffectforspecies11limber.Thereisextensiveresearchondifferentialequationswithtimedelaybutthereisoillylittleworkdoneondifferenceequationswithtimedelay.Ouraimistoestablishstabi…     

数值求解多延迟中立型系统的渐近稳定性

给出并证明了多延迟中立型系统渐近稳定的克分条件；分析了用线性多步法求解多延迟中立型系统数值解的稳定性，基于Lagrange插值，证明了数值求解多延迟中立型系境的线性多步法渐近稳定的充分必要条件是它是A-稳定的．     

INTERPOLATED FINITE ELEMENT METHODS FOR SECOND ORDER HYPERBOLIC EQUATIONS AND THEIR GLOBAL SUPERCONVERGENCE

We develop the interpolated finite element method to solve second-order hy-perbolic equations. The standard linear finite element solution is used to generate a newsolution by quadratic interpolation over adjacent elements. We prove that this interpo-lated finite element solution has superconvergence. This method can easily be applied togenerating more accurate gradient either locally or globally, depending on the applications.This method is also completely vectorizable and parallelizable to take the advantages ofmodern computer structures. Several numerical examples are presented to confirm ourtheoretical analysis.     

等式约束的凸非线性规划问题降维算法

对等式约束的凸非线性规划问题的非线性方程组算法进行了研究.从一般等式约束问题的最优性条件出发,构造一个非线性方程组,解此方程组便可求得非线性规划问题的最优解.     

Novel method based on ant colony opti mization for solving ill-conditioned linear systems of equations

1 .INTRODUCTIONStudies have shownthat some systems are highlysen-sitive :a small perturbationin the data can result in alarge changeinthe solutions .Such systems are calledill-conditioned systems .Ill-conditionedlinear systemsof equations have a wide application in many fieldssuch asi magine processing,deconvolution, model pa-rameters esti mation.Because the condition number ofill-conditionedlinear systems of equationsis very big,the data error andthe rounding error inthe computa-tional p…     

非线性中立型延迟微分方程的散逸性

主要研究非线性中立型延迟微分方程本身及其数值方法的散逸性问题。首先,对此类中立型延迟微分方程理论解的散逸性给出了充分条件;随后,应用一类线性多步法求解至该类问题,证明了在适当条件下,其数值解也具有散逸性;最后,数值试验进一步验证了理论结果的正确性。     

Newton type methods for solving nonsmooth equations

1.INTRODUCTION Thenonsmoothequationsproblemplaysanimportant roleinengineering,systemanalysis,management scienceandetc.Manypublicationsdealtwiththe methodsforsolutionofnonsmoothequations,see Refs.[1～4].Letusconsiderthesystemofnons moothequations F(x)=0(1)whereF∶Rn→RmislocallyLipschitzian.NewtonmethodsforsolvingthenonsmoothEq.(1)aregiven asfollows xk+1=xk-V-1kF(xk)(2)whereVkisanelementofvarioussubdifferentialsof Fatxk,forinstance,Clarkesubdifferential[1],B differential[2],b differen…     

RESIDUAL A POSTERIORI ERROR ESTIMATE OF A NEW TWO-LEVEL METHOD FOR STEADY NAVIER-STOKES EQUATIONS

Residual-based a posteriori error estimate for conforming finite element solutions of incom-pressible Navier-Stokes equations,which is computed with a new two-level method that is differentfrom Volker John,is derived.A posteriori error estimate contains additional terms in comparison tothe estimate for the solution obtained by the standard finite element method.The importance of theadditional terms in the error estimates is investigated by studying their asymptotic behavior.For opti-mal scaled meshes,these bounds are not of higher order than the convergence of discrete solution.Thetwo-level method aims to solve the nonlinear problem on a coarse grid with less computational work,then to solve the linear problem on a fine grid,which is superior to the usual finite element methodsolving a similar nonlinear problem on the fine grid.     

阵列声波测井成像迭代算法及仿真研究

利用阵列声波测井中的反射初至波可以对井孔附近目标体速度结构进行成像，采用离散图象重建技术将成像问题经过线性化处理转化为线性方程组的求解。由于其方程组一般是病态、无精确解的，为此探讨了一种求解任意线性方程组的简单、实用的迭代算法以及其收敛J胜，该算法不需矩阵求逆而总能得到最优解。经过一些典型类型的仿真分析，结果表明该算法在处理声波射线数据不足的情况下能获得理想的成像效果。     

Runge-Kutta方法求解结构动力学方程

将几种具有不同稳定性的Runge-Kutta方法应用到结构动力学方程的数值求解中。针对增量形式的动力学方程,使用改进的Newton-Raphson迭代,研究了减少计算量的两种方法：（1）使用单对角隐式Runge-Kutta方法,（2）应用转化矩阵。采用逼近算子的谱半径分析了稳定性与数值阻尼特性,解释了L-稳定方法抑制高频振荡的原因。数值算例表明在精确解上较小的物理阻尼能有效的抑制高频振荡,但对各种直接积分方法的影响很小,高精度的L-稳定Runge-Kutta方法能在有效抑制高频振荡的同时高精度的求解低频振动。

Abstract：

Several Runge-Kutta methods with the different stability were applied to solve the equations of motion in structural dynamics. For incremental dynamical equations,using the modified Newton-Raphson iteration,two methods to reduce the amount of work were proposed. The first one is the singly diagonally implicit Runge-Kutta methods,and the second one is to apply the transform matrix. Using the spectral radii of approximation operators,the stability analysis and the numerical damping property were studied,and the reason why the L-stability methods could wipe out the high oscillations was explained. Numerical example was solved by several direct integration methods,the result show that the small physical damping can wipe out high oscillations effectively on exact solution,but it has little effect on numerical solution,and the high order L-stability Runge-Kutta methods can wipe out the high oscillation effectively,at the same time,solve the vibration of low frequencies with high accuracy.     

一类组合两步连续RK-Rosenbrock方法

对于一个大的刚性延迟微分方程系统,除了延迟分量给予系统影响外,还常常会出现系统的解分量有的变化很快,而有的变化很慢的情况。此时,可以把大的刚性延迟微分方程系统分解成为两个耦合的子系统,一个是描述系统快变部分的刚性延迟子系统,另一个是描述系统慢变部分的非刚性延迟子系统。对于分解的刚性延迟微分方程大系统,构造了一类用于求解刚性延迟微分方程的组合两步连续RK-Rosenbrock方法,讨论了方法的构造,方法的阶条件,证明了方法的收敛性,分析了方法的稳定性,数值试验表明方法是有效的。     

Theoretical Computation of Nonlinear System Equations of Heavier Pellets Movements for Two Phase Flow

This paper presents nonlinear ordinary differential equations (ODES) of the heavier pellets movement for two phase flow, which actually represent a system of equations. The usual methods of solution such as Runge -Kutta method and it's datum results are discussed. This paper solves ODES of general form using variable mesh-length, linearizing the nonlinear terms by finite analysis method, fuilding an iteration sequence, and amending the nonlinear terms by iteration . The conditions of convergent operation of iteration solution is checked. The movement orbit and velocity of the pellets are calculated. Analysis of research results and it's application examples are illustrated.     

METHODS FOR IMPROVING APPROXIMATE ACCURACY FOR HYPERBOLIC INTEGRODIFFERENTIAL EQUATIONS

1.IntroductionIn[1],wedealtwiththeglobalextrapolationandcorrectionmethodsfortheparabolicintegrodifferelltialequationandobtainedtheapproximatesolutionsofthirdorder.Nowwepayourattentiontothefollowinghyperbolicintegrodifferentialequationwherefiisarectangular…     

A Multistep Finite Volume Method with Penalty for Thermal Convection Problems in Two or Three Dimensions

The author considers a thermal convection problem with infinite Prandtl number in two or three dimensions. The mathematical model of such problem is described as an initial boundary value problem made up of three partial differential equations. One equation of the convection-dominated diffusion type for the temperature, and another two of the Stokes type for the normalized velocity and pressure. The approximate solution is obtained by a penalty finite volume method for the Stokes equation and a multistep upwind finite volume method for the convection-diffusion equation. Under suitable smoothness of the exact solution, error estimates in some discrete norms are derived.     

Preconditioned method in parallel computation

1.INTRODUCTIONDecreasing the ti mes of communication andincreasingthe rate of it in the whole domain is very i mportantfor i mproving the rate of parallel computation in de-composed domain.Preconditioned technology hasbeen used widelyin this area[1]because it can changethe mode of communication andi mprove the topologi-cal configuration.Orthogonalization is a perfect pre-conditionedtechnology,but it isi mpossibleto orthog-onalize entirely for the large workload of computationand effect of …     

常微分方程初值问题并行算法研究现状

本文对常微分方程初值问题数值求解的并行算法进行综述,给出并行算法的应用前景和构造的一些途径,同时指出并行化的主要困难和一些解决的方法。