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.     

Cpa空间中的非线性逼近

In this paper, we establish the following Jackson and Bernstein inequalities for C_p^a space:(?)where σ=(α+ (1/p)^-1),α > 0,0 < p < ∞. Moreover, these inequalities are used to give characterizations of the approximation spaces resulted from two approximations verpectively by splines with free knots and approximation by rational functions.     

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。     

非线性广义加权逼近

本文对一类“几乎最大”的集族分别给出广义权函数最佳逼近的Koimogorov型和交错型特征定理．     

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.     

用矩阵符号函数解(广义)周期Sylvester方程

(广义)周期Sylvester方程来源于周期离散线性系统. 本文主要研究这类方程满足特征值分别位于开左半复平面和开右半复平面或位于单位圆周内和单位圆周外条件时用矩阵符号函数求解的数值方法.并通过数值例子说明我们的结论.     

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…     

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.     

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.     

双正侧函数的非线性带位移边值问题

Ｃｌｉｆｆoｒｄ分析中的双正则函数是一类广义正则函数,它的研究是近年来函数论领域内的一个热门分支,本文研究双正则函数的非线性带位移的边值问题．设计积分算子,将边值问题转化成积分方程问题,借助于积分方程理论和Ｓｃｈａｕｄｅｒ不动点理论证明了边值问题解的存在性并给出了解的积分表达式．