某可微函数类在Orlicz空间内的宽度估计

本文首先研究了Υ阶广义样条类在Orlicz空间内的极值问题,由此进一步考虑了光滑函数类Ω_∞~Υ[0,1]在Orlicz空间内的n宽度的精确估计问题.最后还讨论了相应的对偶情形.     

关于紧光滑流形上半鞅随机微分方程在欧氏空间的嵌入

关于微分流形上随机微分方程的显式解结构研究,上直是随机分析学中倍受关注的问题。文[3]借助光滑流形上非退化椭圆算子产生Riemann度量的思想,把光滑流形上具有非退化扩散项的随机微分方程提升到光滑流形的正标架丛上,从而给出了随机微分方程的     

一个基于罚方程的二阶锥线性互补问题的广义牛顿法

<正>1引言二阶锥线性互补问题是线性互补问题的推广,在工程设计、控制、金融、经济和管理等领域有着广泛的应用,这使得二阶锥线性互补问题成为数学规划中的一个十分热门的课题.许多学者对二阶锥线性互补问题进行了研究,提出了诸如内点法、矩阵分裂法、光滑牛顿法、半光滑牛顿法等算法~([1-4]).进一步掌握和研究二阶锥线性互补问题的各类算法不仅具有理论意义,而且具有实际意义.     

关于非线性初边值问题的奇摄动(Ⅰ)

本文研究一类n维拟线性双曲-抛物型方程,具有非线性初边值条件的奇摄动问题。证明了在摄动问题光滑解存在的区域内,具有一致有效的一阶渐近展开式。它以退化问题的充分光滑解为首项,而在t=0附近则出现边界层。所用方法为两变量展开直接构造边界层的方法。同时建立了相应的能量不等式,进而导出其余项在某种模意义下的估计式:‖Z‖=O(ε~2)。本文拓广了文[2—4]的工作。     

求解无限维非线性互补问题的光滑化牛顿法

研究一类无限维非线性互补问题的光滑化牛顿法.借助于非线性互补函数,将无限维非线性互补问题转化为一个非光滑算子方程.构造光滑算子逼近非光滑算子,在光滑逼近算子满足方向可微相容性的条件下,证明了光滑化牛顿法具有超线性收敛性.     

一个基于罚方程的线性互补问题的广义牛顿法

<正>1引言线性互补问题是运筹学与计算数学的一个交叉研究领域,已经广泛应用于力学、交通、经济、金融、控制等领域中出现的许多数学模型,例如障碍和自由边界问题、供应链问题、交通分配问题、经济均衡问题、非均衡博弈论等,这使得线性互补问题成为数学规划中的一个十分热门的研究课题.许多学者对线性互补问题的求解进行了深入的研究,提出了许多算法[1-4],例如:投影法、光滑牛顿法、非光滑牛顿法、松弛法、内点法、非光     

关于非线性初边值问题的奇摄动(Ⅱ)

本文研究一类拟线性双曲—抛物型方程,具有变动边界的初边值问题的奇摄动:在某些条件成立,且ε充分小时,此问题的解具有以退化问题充分光滑解为首项的广义渐近展开式(Van der Corput意义),它在充分光滑解存在的区域Q={(x,t)|l₀(t)≤x≤l₁(t),0≤t≤T}上一致有效.其边界层存在于t=0附近.本文是工作[3]～[5]的进一步发展.     

Orlicz空间内正系数代数多项式倒数对非负连续函数的逼近

本文研究了Bernstein-Durrmeyer代数多项式倒数对非负连续函数在Orlicz空间中的逼近问题.利用光滑模和K-泛函等工具,获得了收敛速度的估计,所得的结果比Lp空间内的相应结果具有拓展的意义.     

一阶拟线性非齐次偏微分方程存在整体光滑解的条件

在文献[1],[2]中讨论了一阶拟线性齐次偏微分方程 Cauchy 问题(1)(2)关于整体光滑解的存在性问题.文献[1]得到了λ_i=λ_i(u)时 Cauchy 问题(1)、(2)存在整体光滑解的充要条件;文献[2]进而得到了λ_i=λ_i(t,x,u)时 Cauchy 问题(1)、(2)存在整体光滑解的充要条件。本文将用[1]、[2]的思想方法,讨论一阶拟线性非齐次偏微分方程 Cauchy 问题     

一个新的求解加权线性互补问题的非单调光滑牛顿法

本文研究了求解加权线性互补问题的光滑牛顿法.利用一类光滑函数将加权线性互补问题等价转化成一个光滑方程组,然后提出一个新的光滑牛顿法去求解它.在适当条件下,证明了算法具有全局和局部二次收敛性质.与现有的光滑牛顿法不同,我们的算法采用一个非单调无导数线搜索技术去产生步长,从而具有更好的收敛性质和实际计算效果.     

THE FINITE ELEMENT METHOD FOR SEMILINEAR PARABOLIC EQUATIONS WITH DISCONTINUOUS COEFFICIENTS

1.IntroductionLetxbepointsonplaneR',andfibeapolygonaldomain,wedenotetheboundaryoffibyOff.Thereinfiarefinitemanybrokelineswhichdivideitilltofinitepolygonalsubdomainsall,I=1,''jL.Thefunctionp(x)EL'(fl)isassumedtohaveboundedfirstderivativesinallsubdomainsall,whilepisallowedtobediscontinuousontheinterfacesoflinOflj.AndthereexistsapositiveconstantTsuchthatp(x)2T)Vxefi.WeadopttheusualnotationsoftheSobolevspacesinthispaper,thatis,denotebyH'(fl)andHI(fl)thespacesand11'11.thenorms,l'1.theseminor…     

高维复域中具非正则奇异性的非线性偏微分方程的形式解

本文在C_t×C_x~n上研究一类一阶具非正则奇异性的非线性偏微分方程.在一定条件下,证明了其形式幂级数解属于形式Gevrey类,并给出了其Gevrey类指标的精确刻画.     

A numerical method for solving the time fractional Schrödinger equation

In this article, we proposed a new numerical method to obtain the approximation solution for the time-fractional Schrödinger equation based on reproducing kernel theory and collocation method. In order to overcome the weak singularity of typical solutions, we apply the integral operator to both sides of differential equation and yield a integral equation. We divided the solution of this kind equation into two parts: imaginary part and real part, and then derived the approximate solutions of the two parts in the form of series with easily computable terms in the reproducing kernel space. New bases of reproducing kernel spaces are constructed and the existence of approximate solution is proved. Numerical examples are given to show the accuracy and effectiveness of our approach.     

New a posteriori error estimates for singular boundary value problems

In this paper, we discuss the asymptotic properties and efficiency of several a posteriori estimates for the global error of collocation methods. Proofs of the asymptotic correctness are given for regular problems and for problems with a singularity of the first kind. We were also strongly interested in finding out which of our error estimates can be applied for the efficient solution of boundary value problems in ordinary differential equations with an essential singularity. Particularly, we compare estimates based on the defect correction principle with a strategy based on mesh halving. AMS subject classification 65L05Supported in part by the Austrian Research Fund (FWF) grant P-15072-MAT and SFB Aurora.     

A generating functionology approach to a problem of Wilf

Wilf posed the following problem: determine asymptotically as n→∞ the probability that a randomly chosen part size in a randomly chosen composition of n has multiplicity m. One solution of this problem has been given by two of the authors 〈http://www.csc.ncsu.edu/faculty/savage/〉. In this paper, we study this question using the techniques of generating functions and singularity analysis.     

Existence and regularity of solution to the generalized Tricomi equation with a singular initial datum at a point

In this paper, we study the existence and regularity of a solution to the initial datum problem of a semilinear generalized Tricomi equation in mixed-type domain. We suppose that an initial datum on the degenerate plane is smooth away from the origin, and has a conormal singularity at this point, then we show that in some mixed-type domain, the solution exists and is conormal with respect to the characteristic conic surface which is issued from the origin and has a cusp singularity.     

边裂纹柱扭转的强奇性积分方程解法*

本文利用单裂纹扭转的位错型解答,使用有限部积分的概念和方法,最后将含有单根水平裂纹的柱体扭转问题归为解一个强奇性积分方程,并为其建立了数值求解方法,文末作了若干数值例子的计算,结果令人满意.     

非正则奇异性偏微分方程组的形式解

本文研究了在复空间Ct×Cx上一类具有非正则奇异性的偏微分方程组的问题.利用形式Borel变换的方法,在一定的条件下,获得了在复空间Ct×Cx的原点附近的某个邻域内存在唯一的形式解,且该形式解属于某Gevery类,并给出了该Gevery类的指标,推广了非正则奇异性偏微分方程的研究结果.     

Geometry of singularities for the steady Boussinesq equations

Analysis and computations are presented for singularities in the solution of the steady Boussinesq equations for two-dimensional, stratified flow. The results show that for codimension 1 singularities, there are two generic singularity types for general solutions, and only one generic singularity type if there is a certain symmetry present. The analysis depends on a special choice of coordinates, which greatly simplifies the equations, showing that the type is exactly that of one dimensional Legendrian singularities, generalized so that the velocity can be infinite at the singularity. The solution is viewed as a surface in an appropriate compactified jet space. Smoothness of the solution surface is proved using the Cauchy-Kowalewski Theorem, which also shows that these singularity types are realizable. Numerical results from a special, highly accurate numerical method demonstrate the validity of this geometric analysis. A new analysis of general Legendrian singularities with blowup, i.e., at which the derivative may be infinite, is also presented, using projective coordinates.Research supported in part by the ARPA under URI grant number #N00014092-J-1890.Research supported in part by the NSF under grant number #DMS93-02013.Research supported in part by the NSF under grant #DMS-9306488.     

The Superconvergence of the Composite Trapezoidal Rule for Hadamard Finite Part Integrals

The composite trapezoidal rule has been well studied and widely applied for numerical integrations and numerical solution of integral equations with smooth or weakly singular kernels. However, this quadrature rule has been less employed for Hadamard finite part integrals due to the fact that its global convergence rate for Hadamard finite part integrals with (p+1)-order singularity is p-order lower than that for the Riemann integrals in general. In this paper, we study the superconvergence of the composite trapezoidal rule for Hadamard finite part integrals with the second-order and the third-order singularity, respectively. We obtain superconvergence estimates at some special points and prove the uniqueness of the superconvergence points. Numerical experiments confirm our theoretical analysis and show that the composite trapezoidal rule is efficient for Hadamard finite part integrals by noting the superconvergence phenomenon. The work of this author was partially supported by the National Natural Science Foundation of China(No.10271019), a grant from the Research Grants Council of the Hong Kong Special Administractive Region, China (Project No. City 102204) and a grant from the Laboratory of Computational Physics The work of this author was supported in part by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 102204).