非线性发展型方程的Legendre拟谱逼近

本文考虑非稳态Burgers方程的拟谱逼近，构造了一类Legendre拟谱计算格式并证明了其收敛性，数值结果显示了格式的有效性。     

绝对值函数的一致光滑逼近函数

绝对值函数是一个非光滑函数,研究了绝对值函数的光滑逼近函数.给出了绝对值函数的上方一致光滑逼近函数和下方一致光滑逼近函数,分别研究了其性质,并通过图像展示了逼近效果.     

基于Legendre函数的Landau''''s型不等式

首先研究了L2w(-1,1)上关于Legendre多项式Xn(x)的Landau's型不等式.利用Xn(x)的正交性,建立了代数多项式pn(x)的Landau's型不等式,并且指出其不等式的系数在某种意义上是最好可能的.     

关于连续素数上取值的Legendre符号和的估计

利用Karatsuba的方法,研究了关于连续素数上取值的Legendre符号和∑p≤N(p q)的估计问题,得到了当q0.75+ω相似文献   

Legendre小波函数求解非线性Volterra积分微分方程组的数值解

Legendre小波函数被用于逼近非线性Volterra积分微分方程组的解,方法是基于Legendre小波的性质构建相应的积分算子矩阵,进而将原问题转化为关于未知解系数的线性方程组,通过求解该方程组,即得原问题的数值解.数值结果表明所述方法对于求解此类问题是行之有效的.     

多元函数的最佳逼近递减的逼近阶

关于找一个必要与充分条件使得ωｉ１…ｋｉｍ（ｆ,１σｉ１,…,１σｉｍ）～Ｙσｉ１…σｉｍ（ｆ）,（σｉｊ→∞）成立的Ｔｉｍａｎ问题被解决。这条件是ωｋ１…ｋｉｍ（ｆ,δｉ１…δｉｍ）～ωｋｉ１＋１,…,ｋｉｍ＋１（ｆ,δｉ１…δｉｍ）,（δｉｊ→０）。     

非线性最优控制的反馈逼近

本文将在线性最优控制中经典的Ｋｌｅｉｎｍａｎ－Ｎｅｗｔｏｎ［１］方法推广到非线性的最优控制问题。我们证明,由一个稳定反馈控制生成的反馈控制序列在原点附近会一致逼近最优控制,并指出这一研究在Ｈ∞－非线性最优控制中的作用。     

论非线性多重网格法的逼近性质

多重网格法是一种求解椭圆边值问题离散所得的大型线性或非线性方程组的“最优”解法。在有限元离散情形,Hackbusch提出了一种多重网格法的收敛分析方法,即把线性或非线性的多重网格法收敛率的估计问题归结为所谓“光滑性质”与“逼近性质”的研究。在线性情形,若已知有限元解的误差估计,一般容易得到多重网格法的“逼近性质”。但对非线性多重网格法的“逼近性质”在什么条件下成立,尚未见到这方面的工     

基于F-算子的函数逼近的推广与改进

Through the further study on the problems of F-operator in this paper, some research results for f(x) approximated by F(f,x) are extended, some are refined precisely; meanwhile, the constant is improved further.     

THE PREDICTION-CORRECTION LEGENDRE COLLOCATION METHOD FOR NONLINEAR EVOLUTIONARY PROBLEMS

The initial-boundary value problem of Burgers equation is considered. A prediction-correction Legendre collocation scheme is presented, which is easy to be performed. Its numerical solution possesses the accuracy of second-order in time and higher order in space. Numerical results are reported, which show the high accuracy of this approach. The techniques used in this paper are also applicable to other nonlinear evolutionary problems.     

SOME NONLINEAR APPROXIMATIONS FOR MATRIX-VALUED FUNCTIONS

Some nonlinear approximants, i.e., exponential-sum interpolation with equal distance or at origin, (0,1)-type, (0,2)-type and (1,2)-type fraction-sum approximations, for matrixvalued functions are introduced. All these approximation problems lead to a same form system of nonlinear equations. Solving methods for the nonlinear system are discussed.Conclusions on uniqueness and convergence of the approximants for certain class of functions are given.     

THE PREDICTION-CORRECTION LEGENDRE SPECTRAL SCHEME FOR NONLINEAR EVOLUTIONARY PROBLEMS*

The initial-boundary value problem of Burgers equation is considered. A prediction-correction Legendre spectral scheme is proposed. It possesses the accuracy of second order in time and higher order in space. The numerical experiments show the high accuracy of this approach.     

LEGENDRE SPECTRAL-FINITE ELEMENT METHOD FOR THE THREE-DIMENSIONAL UNSTEADY NAVIER-STOKES EQUATION

This paper is devoted to the mixed Legendre spectral-finite element approximation of the three-dimensional, non-periodic, unsteady Navier-Stokes equations. A class of fully discrete schemes are constructed with artificial compression. The generalized stability and convergence are proved strictly on the assumption that the two-dimensional inf-sup condition of the finite element approximation is satisfied.     

COMBINED LEGENDRE SPECTRAL-FINITE ELEMENT METHOD FOR THE TWO-DIMENSIONAL UNSTEADY NAVIER-STOKES EQUATION

1.IntroductionThereismuchliteratureconcerningnumericalsolutionsofNavier-Stokesequations,e.g.,see[1--4].FOrsemi-periodicproblems,someauthorusedcombinedFOurierspectralfinitedifferenceandFOurierspectral--finiteelementapproximations(see[5--8]).Influiddyn...     

非线性微分系统的反射函数与周期解(英文)

1 IntroductionAs is well known, in the objective world the motion of many objects canoften be described by differentia1 systemThe study of the regularity of this motion needs only to discuss the pro-perty of the solutions of system (1). In ear1y eighties Russian mathematicianV.I.Mironenko was the first to establish the theory of reflective function (RF).Since then a new method has been estab1ished.Assume that X(t, x) is a continuously differentiable function on R x R",and that there exists…     

EXISTENCE AND ITERATIVE APPROXIMATIONS OF BOUNDED POSITIVE SOLUTIONS TO A NONLINEAR NEUTRAL DIFFERENTIAL EQUATION

In this paper,we consider a nonlinear neutral differential equation.By the Schauder fixed point theorem,some sufficient conditions are obtained to ensure the existence of uncountably many bounded positive solutions.In addition,we give the iterative approximation sequences with errors for these positive solutions and establish some error estimates between the approximate and the positive solutions.     

ON SIGN FUNCTION AND SQUARE ROOT METHODS FOR SOLUTION OF REAL ALGEBRAIC RICCATI EQUATIONS

In this paper, we first justify the theory of the square root algorithm presented in [1], [2] by simple application of the matrix sign function, then we present an iterative square root algorithm for the continuous time algebraic Riccati equation.     

带奇函数因子的数值积分公式

1 引言 在物理学中常会遇到integral from n=-T to T(f(x)φ(x)dx)型的数值积分问题,其中φ(x)在[-T,T]上为奇函数,亦即φ(-x)=-φ(x),比如振荡函数的积分integral from n= x to -x(f(x)sinwxdx)就是最典型的情况,本文把此型积分称为带奇函数因子的积分,由于φ(x)在[-T,T]上符号有正有负,故在[-     

一类非线性映象的Yosida近似与渐近性质

设Ａ为自反Ｂａｎａｃｈ空间Ｘ上的任意极大单调映象，Ｊ为Ｘ到Ｘ的正规对偶映象，本文对复合映象Ｂ＝ＪＡ＾－ＩＪ定义其Ｙｏｓｉｄａ近似和预解式算子，并证明它们的若干渐近性质，作为应用，指出对Ｆ．Ｅ．Ｂｒｏｗｄｅｒ单调算子构造可解性问题的化简及对Ｒ．Ｔ．Ｒｏｃｋａｆｅｌｌａｒ，Ｇ．Ｋａｓｓａｙ的邻近点算法收敛性结果的推广。