求解常微分方程初值问题的并行块隐式Runge—Kutta方法

本文针对多处理机系统构造了一类并行块隐式Runge-Kutta方法。在S=2的情况下,给出了几个具有三阶精度的并行计算公式,并证明了这类公式具有A稳定性,数值结果表明该计算公式对求解刚性常微分方程是有效的。     

一类并行块隐式方法

本文针对多处理机系统构造了一类并行块隐式方法。具体地给出了此类方法的一个具有两个进程和二阶精度的并行计算公式,并证明了该计算公式具有A稳定性,数值结果表明该计算公式对求解刚性常微分方程是有效的。     

多步块格式求解微分-代数方程

多步块格式是一类新的一般线性方法,在求解微分-代数方程的过程中不会出现精度降低现象。研究了多步块格式的构造方法,精度条件及具有Runge-Kutta稳定性的多步块格式,多步块格式具有刚性精确的优点,且级精度与格式精度相等。构造了具有Runge-Kutta稳定性的2级和3级多步块格式,具有L-稳定性。数值算例证实多步块格式在求解微分-代数方程不会精度降低。

Abstract：

The multistep block methods are a new class of general linear methods,and the methods solve the differential-algebraic equations with no order reduction.The construction of the multistep block methods was described,and order condition and stability was studied.The multistep block methods with Runge-Kutta stability were also constructed.The multistep block methods have many nice properties,for example,stiffly accurate,and stage order is equal to order of method.At last the methods of 2-stage and 3-stage with Runge-Kutta stability were constructed,and they have the property of L-stability.The numerical example shows that the multistep block methods can solve the differential-algebraic equations without the order reduction.     

线性随机微分方程的全隐式Euler方法

由于随机微分方程的全隐式Euler方法不是均方收敛的,一般认为它没有意义.然而,从运用计算机实现的角度来说几乎处处意义下的收敛和稳定比均方意义的收敛和稳定更具优势.针对线性随机微分方程,提出了一类全隐式Euler方法,证明了该方法生成的数值解几乎处处收敛,给出了该方法几乎处处稳定的充要条件.     

关于抛物型方程的一种线条法

本文对于热传方程运用线条法形成常微分方程系统:就空间变量的离散化,二阶偏导数项在邻接左、右边界的两根线条上采用三点对称格式〔截断误差为O(h~2)〕,在中间其余线条上采用五点对称格式〔截断误差为O(h~4)〕,注意到常微分方程组的系数阵具有全为负的本征值,本文应用A_0一稳定的P阶线性方法,证明数值解与偏微分方程精确解之间整体误差可达O(h~(4p)/(p+1)),接近O(h~4)。这表明,在有局部的低阶离散化误差的情况下仍可获得高阶的整体误差。     

一类并行隐式Runge-Kutta公式

本文针对多处理机系统构造了一类并行隐式Runge-Kutta公式,对2级Runge-Kutta公式给出具有4阶精度的公式族,并证明了它们的收敛性,进行稳定性分析。数值例子表明,该公式可以有效地数值求解较广泛类型的常微分方程初值问题。     

基于级差格式的GM(2,1)模型参数估计优化研究

参数估计的优化是提高灰色模型精度的一个重要途径,级差格式的提出避免了背景值的复杂构造.现有的GM(2,1)模型计算较为复杂,且参数估计基于目标函数是原始序列一次差分序列的拟合误差平方和最小化来确定,同时,参数估计中微分到差分的转换以及背景值构造存在较大误差.针对这些问题,本文基于GM(2,1)模型微分方程的时间响应函数推导了级差格式,给出了最小二乘法的参数估计方法,然后基于原始序列误差平方和最小的目标函数,优化了模型的两个初始条件,同时,推导出GM(1,1)回归模型和GM(1,1,exp)模型是该模型的特殊情况,最后通过实例比较本文优化方法与现有方法估计的GM(2,1)模型拟合精度与预测精度.实例结果显示,本文的优化方法估计的GM(2,1)模型具有较好的效果.     

一类并行隐式Runge-Kutta方法的A稳定性分析

本文针对多处理机系统构造了一类并行隐式Runge—Kutta方法,给出了一个具有三阶精度的并行二级Runge—Kutta公式,并证明了该计算公式具有A稳定性,数值结果表明该计算公式对求解刚性常微分方程是有效的。     

求解延迟微分方程块θ-方法的GPLm-稳定性

讨论了带有多个滞时量的延时微分方程的数值稳定性,分析了用块θ–方法求解多延迟微分方程GPm–稳定和GPLm–稳定的条件,基于Lagrange插值,证明了块θ–方法GPm–稳定的充分必要条件是方法是A-稳定的,块θ–方法GPLm–稳定的充分必要条件是θ=1。     

迟滞非线性系统自适应鲁棒控制

介绍用超磁致伸缩材料与压曲放大机构组合设计的微位移驱动器,并设计了控制系统.建立了超磁致伸缩执行器基于输入电压-输出位移的机电系统传递函数模型.对微位移驱动器的迟滞特性用微分方程建立了模型.在此基础上构造迟滞模型与传递函数相结合的系统模型.由滑模控制理论,对所建模型提出了可以调节信号跟踪精度的自适应鲁棒控制方法,用Lyapunov稳定性理论进行了系统稳定性证明.通过系统模型仿真与simulink中的半实物仿真实现了该控制率,并验证了模型的准确性和补偿控制的有效性.     

NONHOMOGENEOUS HOPF EQUATIONS IN HIGHER DIMENSIONS

1.IntroductionWeconsiderthefollowingequationsHeretheunkownfunctionisu~(ul,u2)'',u.)andu'V~Z:=,nib.Whenn~1,(1.1)isBurger'sequationwithviscosityeand(1.2)isHopfequationwithnonhomogeneoustermb(x,t).Ladyzhenskayahajsinvestigatedtheinitial-boundaryvalueproblom…     

Monotone Iterative Technique for Boundary Value Problem of Second Order Singular Differential System

ＭｏｎｏｔｏｎｅＩｔｅｒａｔｉｖｅＴｅｃｈｎｉｑｕｅｆｏｒＢｏｕｎｄａｒｙＶａｌｕｅＰｒｏｂｌｅｍｏｆＳｅｃｏｎｄＯｒｄｅｒＳｉｎｇｕｌａｒＤｉｆｆｅｒｅｎｔｉａｌＳｙｓｔｅｍＷＡＮＧＷｅｉ；ＬＩＵＹｏｎｇｑｉｎｇ（Ｄｅｐｔ．ｏｆＡｕｔｏｍａｔｉｏｎ...     

H 2/H ∞ control problems of backward stochastic systems

This paper is concerned with the mixed H2/H∞ control problem for a new class of stochastic systems with exogenous disturbance signal.The most distinguishing feature,compared with the existing literatures,is that the systems are described by linear backward stochastic differential equations（BSDEs）.The solution to this problem is obtained completely and explicitly by using an approach which is based primarily on the completion-of-squares technique.Two equivalent expressions for the H2/H∞ control are presented.Contrary to forward deterministic and stochastic cases,the solution to the backward stochastic H2/H∞ control is no longer feedback of the current state;rather,it is feedback of the entire history of the state.     

A New Algorithm on Sequencing the Importance of Alln Alternatives to an Upper-Level Attribute in AHP

1IntroductionTheanalytic11ierarchyprocess(AHPforshort)isallanalyticmethodindecisionmaking.Itsynthesizedquantitativeandqualitativeanalysismethod,andcallsolvethemulti-objectivedecisionmakingproblemwhichhajsmulti-alternativesandcomplexhierarchystructuresll].Theproblemofsequencingtheimportanceofall11alternativestoanupper-levelattributeHaintermsofagivencriterionscalesisveryimportantandbajsic.ItcanbedescribedasfollowstTherearenalterllativesXI,X2,...,X.andanattributeHk'Accordingtoagivedcriterion…     

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.     

A Proposed Gravitodynamic Theory

1.IntRODUCTIONInarecentreviewPaper,Norton[11hasshownthattheprincipleofgeneralcovariancehasbeendisputedasphysicallyvacuous.ThedebateoverthisprinciplePersiststoday.Ingeneralrelativity,spaCe-timecoordinatescanbearbitrarilychosen[2,3]andgravitationalPOtentialsarerepresentedbythemetrictensof,gp.inthefouredimensional(4ro)lineelement:wheregpvhastenindependentcomPOnents,andGreekletterspandvrunfrom0tO3.InEq.(l),d/isan'invariantunderspace--timecoordinatetransformation.However,inordertogetunique…     

企业环境绩效与经济绩效关系的理论研究与模型构建

通过联立方程模型把环境绩效和经济绩效结合在一起,并借鉴意大利、荷兰及我国某地区造纸行业的数据进行了实证研究,发现这种方法可以验证环境绩效与经济绩效之间的关系,研究结果比较支持传统学派的观点,但这并不表明修正学派的观点没有价值,只是因为本文只针对一个特殊的行业造纸业,而且考察的只是企业短期的经济绩效,如果考虑环境污染给社会带来的外部成本,那么结果可能相反.     

BDF方法解常系数微分代数方程的稳定性分析

本文分析了ＢＤＦ方法解常系数微分代数方程（ＤＡＥ）的稳定性，并且说明了ＢＤＦ方法，数值求解一般高指标微分代数问题时会遇到不可克服的困难。     

An Efficient Approach for Fuzzy Project Network Analysis

1　 IntroductionProject network analysis is a successful instrument in the planning and control of large,complex project.A network G( N,A) is a picture of a project with node set N and arc setA.The network representing the project is acyclic,compact and directed.The nodesstand for the events,while the arcs stand for the activities of the project.Each activity isdefined as a task requiring time for its completion,and each event represents a point intime that signifies the completion of some …     

HARMONIC MAPS VERSUS POISSON EQUATIONS ON NONCOMPACT RIEMANNIAN MANIFOLDS

1.Introducti0llStartingfromtheworkofP.LiandT.F.Taml1'2])therearesomeprogressonthestudyofharmonicmaPsbetweennegativelycurvedc0mplete,noncompactriemannianmanifolds.Wemayquote[2-5]justforafew.Thenewstartingpoilltin[1]isthea-ssumption0fagivenmaPwithitstensi0nfieldinasuitableSob0levspace.Asacomparison,wementi0nthatthekeytechniqueofthemethod0fEells-Sampsonl6]istheuseofaBochnertypeevoluti0n0ftheenergydensitywithaninitialdataoftotalenergy.InthispaPer,wetrytogivealargec1assofapprokimateharmonicma…