NONLINEAR GALERKIN METHOD FOR STEADYNONLINEAR DIFFERENTIAL EQUATIONS

1.IntroductionNonlinearGalerkinmethodsarenumericalschemesforthedissipativeevolutionpartialdifferelltialequationswherethespatialdiscretizationreliesonanonlinearmanifoldinsteadofalinearspaceasintheclassicalGalerkinmethod.Moreprecisely,oneconsidersafinitedim…     

MULTILEVEL CORRECTION FOR COLLOCATION SOLUTIONS OF VOLTERRA NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS

1. IntroductionWe consider a Volterra integro-differential equationwith initial condition u(0) = not where f, P, k are continuous on their respective domainsJ, JxR and axs (n:~ {(t,s): 05s5t5T}) such that (1.l) possesses a unique solutionu E C'(J).It has been shown in [1] that the collocation approximation for (1.1) by discolltinuous piece--wise polynomial spline collocation at the Gauss points restore optimal local superconvergenceat the knots but does not yield global superconvergence on…     

AN EXISTENCE THEOREM FOR RADIAL POSITIVE SOLUTIONS OF NONLINEAR DEGENERATE ELLIPTIC EQUATIONS

ＡＮＥＸＩＳＴＥＮＣＥＴＨＥＯＲＥＭＦＯＲＲＡＤＩＡＬＰＯＳＩＴＩＶＥＳＯＬＵＴＩＯＮＳＯＦＮＯＮＬＩＮＥＡＲＤＥＧＥＮＥＲＡＴＥＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＳＬＩＵＨａｉｌｉａｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｅｎａｎＮｏ...     

THE EXTRAPOLATION METHOD FOR A CLASS OF NON-SMOOTH FREDHOLM INTEGRAL EQUATIONS

For a class of non-smooth Fredholm integral equations we prove thatRichardson extrapolation method can be used to increase accuracy for finite ele-ment methods.On the basis of local refinement mesh,a superconvergence result isshown.Our theory also covers a class of non-smooth Wiener-Hopf equations andan application includes the calculation in certain linear elastic fracture problems.     

ANTI-PERIODIC SOLUTIONS FOR FIRST AND SECOND ORDER NONLINEAR EVOLUTION EQUATIONS IN BANACH SPACES

In this paper, a new existence theorem of anti-periodic solutions for a class ofstrongly nonlinear evolution equations in Banach spaces is presented. The equations con-tain nonlinear monotone operators and a nonmonotone perturbation. Moreover, throughan appropriate transformation, the existence of anti-periodic solutions for a class of second-order nonlinear evolution equations is verified. Our abstract results are illustrated by anexample from quasi-linear partial differential equations with time anti-periodic conditionsand an example from quasi-linear anti-periodic hyperbolic differential equations.     

EXTRAPOLATION FOR FINITE ELEMENT METHODS OF THE FIRST KIND FREDHOLM INTEGRAL EQUATIONS

In this paper,a numerical analysis of finite element methods for Fredholm equationsof the first kind,which is based upon regularization,is made.It shows that extrapolationalgorithms can accelerate the convergence of approximate solutions.     

ON A LINEAR EQUATIONS METHOD OF NONLINEAR POLYNOMIAL EQUATIONS-SOLVING

A method for solving nonlinear polynomial equations is given which avoids theappearance of redundant factors as in the previous characteristic set method developed bythe present author. The new method seems thus to be of much higher efficiency than theprevious one. It has the further advantage that numerical data may be inserted at willeither at the outset or during the procedure so far removal of factors by divisions may beavoided.     

CONVERGENCE PROPERTIES OF DFP METHOD WITH MODIFIED QUASI-NEWTON EQUATIONS

1 IntroductionWe know that in order to obtain a superlinearly convergent method it is necessary to approximate the Newton step asymptotically (see [ll). How can we do this without actually evaluatingthe Hessian matrix by ally approximate to the Hessian matrix at every iteration? The answerwas discovered by Davidonl2] and was subsequently developed and popularized by Fletcher andPowell[3l. It consists of starting with any approximation to the Hessian matrir, and at eachiteration, updating th…     

求解线性三对角方程组的解耦分解方法

本文给出了求解线性三对角方程组的解耦分解方法,并讨论了在计算机上求解的复杂性分析。理论分析和数值实验的结果表明,该解耦分解方法是有效的。特别值得一提的是,对于MIMD多处理机系统,此解耦分解方法是一求解线性三对角方程组的有效并行算法。     

A NEW STABILIZED FINITE ELEMENT METHOD FOR SOLVING THE STOKES AND NAVIER-STOKES EQUATIONS PART II. THE NONLINEAR CASE

1 IntroductionIt is necessary to make some conuneots on some of the re1ated methodologies lately emp1oyedto stabilize the Ga1erkin finite e1ement method for the incompressible NavierStokes equations,including the Stokes equation and the advectiondiffusion problem. Owing to the fact that thehigh Reynold number amounts to a small diffusive term in the advection--diffusion problem,here we will repeatedly mention the diffosion, not the Reynold number or the viscosity in the.. Jincompressible Na…     

ON THE EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS OF VOLTERRA INTEGRAL DIFFERENTIAL EQUATIONS

In this paper,we use the contraction principle and the Leray-Schauder principleto deal with the existence of periodic solutions of the Volterra integral differential equation.Some new existence criteria and unique existence criteria are obtained.     

A NEWTON MULTIGRID METHOD FOR QUASILINEAR PARABOLIC EQUATIONS

A combination of the classical Newton Method and the multigrid method, i.e., a Newton multigrid method is given for solving quasilinear parabolic equations discretized by finite elements. The convergence of the algorithm is obtained for only one step Newton iteration per level. The asymptotically computational cost for quasilinear parabolic problems is O（NNk） similar to multigrid method for linear parabolic problems.     

THE FINITE ELEMENT PROBABILITY COMPUTATIONAL METHOD FOR PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS

1.IntroductionThefiaiteelementprobabilitycomputationalmethodisakindofnumericalcalculationtecboqueofauniquestyle.Themethodshavebeendevelopedduringthefiftiestosixesforuseindeferencemethodll'2'3)andforsolvingsystemofalgebraicequations.Inengineeringandphysicsproblems,oftenwehavetosolvetheconcelltratedloadproblem.Inthiscase,weneedonlytoknowthevaluesofthefunctionatafewnodalpoilltsofthedomain.Itwillwastealotoftimetocomputetheunnecessaryvaluesofthefunctionbythefiniteelemelltmethods(ordeferencemethods…     

POSITIVE SOLUTIONS FOR DIRICHLET PROBLEMS OF SINGULAR SEMILINEAR ELLIPTIC EQUATIONS

ＰＯＳＩＴＩＶＥＳＯＬＵＴＩＯＮＳＦＯＲＤＩＲＩＣＨＬＥＴＰＲＯＢＬＥＭＳＯＦＳＩＮＧＵＬＡＲＳＥＭＩＬＩＮＥＡＲＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＳ￥ＣＵＩＳｈａｎｇｂｉｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＬａｎｚｈｏｕＵｎｉｖｅｒｓ...     

A LIOUVILLE THEOREM FOR GLOBAL SOLUTIONS OF HOMOGENEOUS CAUCHY PROBLEM OF MRABOLIC EQUATIONS

ＡＬＩＯＵＶＩＬＬＥＴＨＥＯＲＥＭＦＯＲＧＬＯＢＡＬＳＯＬＵＴＩＯＮＳＯＦＨＯＭＯＧＥＮＥＯＵＳＣＡＵＣＨＹＰＲＯＢＬＥＭＯＦＭＲＡＢＯＬＩＣＥＱＵＡＴＩＯＮＳ￥ＭＩＮＴａｉｓｈａｎ（ＢｅｉｊｉｎｇＬｉｇｈｔＩｎｄｕｓｔｒｙＩｎｓｔｉｔｕｔｅ，Ｂｅｉ...     

A PRIORI L~2 ERROR ESTIMATES FOR GALERKIN METHODS FOR NONLINEAR SOBOLEV EQUATIONS

In this paper we study Galerkin approximations to the solution of the nonlinearSobolev equation c(u)u_t=▽·{a(u)▽u_t+b(u)▽u}+f(u)in two spatial dimensions and deriveoptimal L~2 error estimates for the continuous-time,Crank-Nicolson and extrapolated Crank-Nicolson discrete-time approximations.     

DESIGN OF NONLINEAR OBSERVERS

ＤＥＳＩＧＮＯＦＮＯＮＬＩＮＥＡＲＯＢＳＥＲＶＥＲＳ￥ＺＨＥＮＧＹｕｆａｎ；ＣＨＥＮＳｈｕｚｈｏｎｇ（ＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓＲｅｓｅａｒｃｈＬａｂｏｒｕｔｏｒｙ，ＥａｓｔＣｈｉｎａＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｓｈａｎｇｈａｉ２００...     

BOUND ON SOLUTIONS TO THE GENERAL SYSTEM OF VOLTERRA－TYPE LINEAR INTEGRAL INEQUALITIES IN SEVERAL VARIABLES AND ITS APPLICATIONS TO INTEGRO－PARTIAL DIFFERENTIAL EQUATIONS

ＢＯＵＮＤＯＮＳＯＬＵＴＩＯＮＳＴＯＴＨＥＧＥＮＥＲＡＬＳＹＳＴＥＭＯＦＶＯＬＴＥＲＲＡ－ＴＹＰＥＬＩＮＥＡＲＩＮＴＥＧＲＡＬＩＮＥＱＵＡＬＩＴＩＥＳＩＮＳＥＶＥＲＡＬＶＡＲＩＡＢＬＥＳＡＮＤＩＴＳＡＰＰＬＩＣＡＴＩＯＮＳＴＯＩＮＴＥＧＲＯ－ＰＡＲＴ...     

ESTIMATION METHOD FOR SOLUTIONS TO GENERAL LINEAR SYSTEM OF VOLTERRA INTEGRAL INEQUALITIES INVOLVING ITERATED INTEGRAL FUNCTIONALS

1. IntroductionThe study of Volterra-type integral inequalities had aroused much research illterest on thepart number of authors. In recent years, various VOlterra inequalities involving iterated illtegralfunctionals have also been investigated. We refer to 11--14] for related results for such inequalitiesin one independent variable. However, there is no result reported in the literature which isconcerned with arbitrary finite systems consisting of such integral inequalities. Obviously suchk…     

A HIGH ACCURACY ANALYSIS OF THE MIXED FINITE ELEMENT METHOD FOR BIHARMONIC EQUATIONS

In this paper,the linear mixed finite element method is considered forthe biharmonic Dirichlet boundary value problem.Almost optimal error estimates,superconvergence estimates and the derivative error expansion are obtained.