解Schrdinger方程的A.D.I.Galerkin方法及其敛速估计

本文提出了解Schrodinger方程的A.D.I.Galerkin方法,证明了解这个方程的Galerin方法及A.D.I.Galerkin方法的收敛性和对初始值的绝对稳定性。 §1 Galerkin方法的收敛性 在分子化学和激光技术中遇到的Schrodinger方程的初边值问题是:     

AN A.D.I.GALERKIN METHOD FOR NONLINEAR PARABOLIC INTEGRO-DIFFERENTIAL EQUATION USING PATCH APPROXIMATION

An A. D. I. Galerkin scheme for three-dimensional nonlinear parabolic integro-differen-tial equation is studied. By using alternating-direction, the three-dimensional problem is reduced to a family of single space variable problems, the calculation is simplified; by using a local approxima-tion of the coefficients based on patches of finite elements, the coefficient matrix is updated at each time step; by using Ritz-Volterra projection, integration by part and other techniques, the influence coming from the integral term is treated; by using inductive hypothesis reasoning, the difficulty coming from the nonlinearity is treated. For both Galerkin and A. D. I. Galerkin schemes the con-vergence properties are rigorously demonstrated, the optimal H~1-norm and L~2-norm estimates are obtained.     

拟线性双曲型方程的A.D.I.Galerkin方法及其敛速估计

§1.引言 本文讨论求解一类二维拟线性双曲型方程的有限元方法([1,4,7]是本文的特殊情形),提出解该方程的 A.D.I.Galerkin方法,并给出最优 H~1模误差估计.[7]中导出了非线性方程组,而本文导出的是U_(ij)~(n+1)的线性方程组.交替方向格式将二维问题化成一维,其计算量比[1,4,7]中诸格式小得多;又在估计误差时,用本文的方法得到的估计式不     

I—ring which Satisfies A.D.C.C on Principal Left Ideals

Derndtl0n1AringRiscalledI-ring,ifasasemigroupRisgeneratedbyitsidemPOtentelements.Defhotl0n2AringRissaidtosatisfyalm0stdescending(0rascending)chaincondi-tionsonleftideals,ifforeverydescending(ascending)chainofleftideals0fR,I,nI2n...nI.Xi..-(I,GI2G...GI'g..-),thereexistsaPOsitiveintegerpsuchthatRPI=Ii(IiGR-'I,)foralli,whereR-'I,={ueRlR'u=IP}.By[5JitisknownthatAringRsatisfiesA.D.C.C(OTA.A.C,C)onleftidealsifandonlyifforeverydescending(0rascending)chalnOfleftidealsofR,I,nI2n-..n…     

对偶扩张代数的Frobenius态射和固定点代数

设A是由箭图Q和关系I所确定的代数,D(A)是代数A的对偶扩张代数, 对应的箭图Q*和关系I*由Q和I决定．本文证明:带关系箭图(Q*,I*)的自同构由带关系箭图(Q,I)的自同构决定;D(A)的Frobenius态射由A的Frobenius态射完全决定;代数D(A)的固定点代数同构于相应的代数A的固定点代数与A°P的固定点代数的张量积,特别地,当Q为单的箭图时,代数D(A)的固定点代数同构于代数A的固定点代数的对偶扩张代数．     

区间AOR方法的收敛性

设A∈I(R~(n×n)是一个区间矩阵,b∈I(R~n)是区间向量.将A分解成 A=D-L-U,其中D,-L和-U分别是A的对角矩阵、严格下和上三角矩阵.假定A的每个对角元均不为零,则可引进求解区间线性方程组     

具有结构阻尼和外阻尼的非自治非线性梁方程的拉回D_δ,E_1-吸引子

考虑了具有结构阻尼和外阻尼的非自治非线性粘弹性梁方程的拉回D_δ,E_1-吸引子.首先利用Galerkin方法,证明了在齐次边界条件和初始条件下系统在V×H和D(A)×V中的整体解的存在唯一性;其次通过先验估计,证明了系统的拉回吸收集的存在性;最后证明了系统满足拉回D_δ,E_1-条件(C),从而证明了系统的强拉回D_δ,E_1-吸引子的存在性.     

带有粘性项Burgers方程解的适定性

这里v>0是粘性系数,c(x,t)是气体速度.这是一个非线性抛物方程的初边值问题.从Galerkin逼近出发,首先根据Caratheodory映象得出Galerkin逼近解c_m(x,t)∈L~∞(Z,L~2(I))∩L~2(Z,H_0~1(I));其次利用实数阶CooeB空间的性质得出相应的Galer-     

2002年数学中考模拟测试题(四)

一、选择题:(本大题满分36分,每小题3分) 】、9的算术平方根是(). A.±3 13.3 c,±压 D.再 2、在平面直角坐标系中,一次函数y=疋z、十厶(七<0,6>0)的图象的大体位置是( ),A B C D 3、若么A=30。,则cosA等于( ). A.譬 B.专 c.譬 D.以 4、如果一个正多边形的内缃和等于540。,那么这个正多边形是( ). A.正三角形 13.正方形 C正五边形 D.正六边形 5、下列各组数中,相等的一组是( ). A.一5和√(一5)。 H.5一’和一5 C一5。和25 I).1—5I和一(一5). 6、oo。和00:的半径分别为2cm和3cm,圆心距o,02:4cnl,那么两圆的位置关系是( ) A.外切 B.…     

算子代数上的Jordan初等映射(英文)

给定两个环R,R’.对于满足一定条件的环R,本文证明了若M:R→R’,M*:R’→R为满射且对A,C∈R和B,D∈R’满足M（AM*（B）C+CM*（B）A）=M（A）BM（C）+M（C）BM（A）,M*（BM（A）D+DM（A）B）=M*（B）AM*（D）+M*（D）AM*（B）则M和M*是可加的;若R和R’分别包含单位I和I’,M（I）,M*（I’）可逆,则存在环同构N使得M（A）=N（A）M（I）,M*（B）=N^-1（BM（I））.特别地,若R=R’为标准算子代数或Hilbert空间套代数,则M和M*可加且存在有界可逆的线性或共轭线性算子S和T使得M（A）=SAT,M*（B）=TBS或M（A）=TA*S,M*（B）=（SBT）*对任意的A,B∈R成立.     

THE FULL DISCRETE DISCONTINUOUS FINITE ELEMENTANALYSIS FOR FIRST-ORDER LINEAR HYPERBOLICEQUATION

1.IntroductionLetfibeaboundeddomaininRZwithpiecewisesmoothboundaryOff,[0,T]beatimeinterval.Considerthefirst-orderhyperbolicproblemasfollowingwhereac~(%,%),p(x,t)~(gi(x,t),pZ(x,t)),Off--(t)~{xEOff:fi(x,t)'ac<0},700istheoutwardunitnormaltoOff;fi(t)~fi\Ofl--(t).Asusual,Off--(t)isreferedtoasinflowboundaryattimet,andOff (t)~Off\Ofl--(t)iscalledoutflowboundaryattimet.FOrsimplicityinfiniteelementanalysis,supposethatboundaryOff--(t)isindependentoft.ThusforalltE(0,T]wecanwriteandproblem(1.0)can…     

一类非线性双曲-抛物耦合问题的A.D.I.Galerkin方法

1　引　言考虑三维非线性双曲 -抛物耦合初边值问题 :utt- . (a1 (X,t,u) u) +b1 (X,t,u,v) . u　　　　 +α1 e. v =f(X,t,u,v) ,X∈Ω,t∈ J.vt-a2 Δv +b2 (X,t,u,v) . v　　　　 +α2 e. ut=g(X,t,u,v) ,X∈Ω,t∈ J.u(X,t) =v(X,t) =0 , X∈ Ω ,t∈ J.u(X,0 ) =u0 (X) ,ut(X,0 ) =ut0 (X) ,v(X,0 ) =v0 (X) ,X∈Ω.(1 .1 )其中 ,X=(x1 ,x2 ,x3) ,Ω=(c1 ,d1 )× (c2 ,d2 )× (c3,d3)为 R3中矩形区域 ,边界 Ω . J=[0 ,T] ,T>0为一正常数 .b1 ,b2 ,f,g均为已知光滑函数 (其中 b1 ,b2 为向量函数 ) ,且关于 u,v满足 L…     

NEW ALTERNATING DIRECTION FINITE ELEMENT SCHEME FOR NONLINEAR PARABOLIC EQUATION

A new alternating direction (AD) finite element (FE) scheme for 3-dimensional nonlinear parabolic equation and parabolic integro-differential equation is studied. By using AD, the 3-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using FE, high accuracy is kept; by using various techniques for priori estimate for differential equations such as inductive hypothesis reasoning, the difficulty arising from the nonlinearity is treated. For both FE and ADFE schemes, the convergence properties are rigorously demonstrated, the optimal H1-and L2-norm space estimates and the 0((△t)2) estimate for time variable are obtained.     

二维抛物型积分微分方程动边界问题的有限元方法

１引言抛物型积微分方程,可广泛用于描述具有记忆的材料的热传导、气体扩散、松散介质中的压力等实际问题中的现象,具有重要研究意义．关于固定空间区域上该类方程的研究,可见文献［１］,［２］;关于动边界抛物型方程,梁国平等已有重要工作［３］,［４］;作者在文［５］中,研究了一维动边界抛物型积微分方程的数值方法．本文研究二维空间区域变动情形下此类方程初边值问题的全离散、半离散有限元逼近格式及有关数值分析．主要特点在于对动边界和时间积分项（Ｖｏｌｔｅｒｒａ项）的处理．对于前者,通过空间变量代换,将问题化为定…     

解高维广义对称正则长波方程的Fourier谱方法

１引言对称正则长波方程（ＳＲＬＷＥ）是正则化长波方程（ＲＬＷＥ）的一种对称叙述［１］用于描述弱非线性作用下空间变换的离子声波传播．［１］得到了方程组（１．１）的双曲正割平方孤立波解、四个不变量和数值结果、明显地,从（１．１）中消去ρ,得到一类正则长波方程（ＲＬＷＥ）代替（１．２）中第三项、第四项对ｔ的导数为对ｘ的导数,得到Ｂｏｕｓｓｉｎｅｓｑ方程．［２］对一类广义对称正则长波方程组提出了谱方法,证明了古典光滑解的存在性和唯一性,建立了近似解的收敛性和误差估计。［３］研究了高维对称正则长波方程整体…     

The numerical solution of a model problem biharmonic equation by using Extrapolated Alternating Direction Implicit methods

The numerical solution of the 2-dimensional biharmonic equation over the unit square by using Extrapolated Alternating Direction Implicit (E.A.D.I.) methods is studied. To approximate the biharmonic equation both a 13-point and a 25-point difference replacements are considered. In each case E.A.D.I. schemes are used together with the acceleration parameter fixed during the iterations or varying according to the Douglas set of parameters. Finally optimum E.A.D.I. schemes are given for every value of the numberN of mesh subdivisions in each co-ordinate direction.     

边界元方法的抽象误差估计及其应用

§1.引言 边界元方法是近二十年来发展的一种求解偏微分方程的数值方法,其基本思想是:先利用Green公式或位势将区域上的偏微分方程转化成边界上的积分方程,此时偏微分方程的解由边界积分方程的解表出;然后数值求解边界积分方程,进而求得偏微分方程的近     

Numerical study of an equation related to wave propagation

We discuss two algorithms for the computation of approximate solutions of a generalization of the so-called Benjamin-Bona-Mahony equation, which is a model proposed to describe unidirectional propagation of long water waves. Both schemes discussed are quadratically convergent with respect to Δt in theH ¹-norm. They use the Galerkin method for the space variable in such a way that the global truncation error has the same order as the error for the interpolation with the Galerkin basis. Estimates are obtained for the study of the discretization that also yield an existence proof for the exact problem. Results of some numerical experiments are presented.     

地下水污染中一离子反应数学模型的有限元方法

1　引　　言在地下水含水层中 ,污染物随地下水运移并常常发生各种化学反应 [1 ] .描述地下水含水层中一类阳离子交换反应 m M1 +r M2 k2k1 r M2 +m M1 的数学模型[2 ] 为 : s1 t- dΔs1 =f1 ,　　 x∈Ω ,t∈ J (1.1a) s2 t- dΔs2 =f2 ,　　 x∈Ω ,t∈ J (1.1b) c1 t+ρ s1 t- DΔc1 =0 ,　　 x∈Ω ,t∈ J (1.2 a) c2 t+ρ s2 t- DΔc2 =0 ,　　 x∈Ω ,t∈ J (1.2 b)其中 Ω R2为具有光滑边界的有界区域 ,J=(0 ,T].这里 D>d>0为扩散系数 ,ρ>0为固体颗粒密度 ,均为常数 .根据 [1,2 ]应有 :f1 =m[k1 Rm1 Rr2 cm1 sr2 -…