奇阶中立型时滞微分方程解的振动性

１．引言考虑奇阶非线性泛函微分方程［ｘ（ｔ）－ｃｘ（ｔ—(）］（ｎ）＋ｐ（ｔ）ｆ（ｘ（ｔ－σ））＝０（１）对方程（１）我们作如下假设（Ｈ）：（Ｈ１）ｎ＞１是奇整数,ｐ∈Ｃ（（ｔ０,∞）,（ｔ０,∞））;（Ｈ２）τ＞０,σ＞０且０≤ｃ≤１;（Ｈ３）ｆ∈Ｃ（Ｒ,Ｒ）是单调增加,ｘｆ（ｘ）＞０,Ｘ≠０且当｜ｘ｜→∞时有｜ｆ（ｔ）｜→∞．设δ＝ｍａｘ｛τ,σ｝,∈Ｃ（［Ｔ－δ,Ｔ］,Ｒ）．方程（１）在［Ｔ,∞）上的解是指函数ｘ∈Ｃ（［Ｔ,∞）,Ｒ）,使得ｘ（ｔ）＝(（ｔ）,Ｔ－δ≤ｔ≤Ｔ,［ｘ（ｔ）－ｃｘ…     

广义中立型系统的渐近稳定性及数值分析

１．引 言 考察如下广义中立型系统：其中,Ｌ,Ｍ,Ｎ ∈ Ｃｄ×ｄ为已知矩阵,　　　为已知向量值函数,　　　　　　　　　　当ｔ＞０时为未知函数,　　　　　　　　　　　　　　　　　　　　　　　　　为常数延时量． 对于　　　　　　　　　　　　　　　　　,１９６７年,Ｂｒａｙｔｏｎ［１］基于Ｌ,Ｍ,Ｎ为实对称矩阵,以及Ｉ± Ｎ和－Ｌ± Ｍ为正定矩阵时,讨论了（１）渐近稳定的充分条件;１９８４年,Ｊａｃｋｉｅｗｉｃｚ［２］基于 Ｌ,Ｍ,Ｎ为复系数时,研究了理论解的渐近稳定性及单步方法的数值稳定性;１９８８年,Ｂ…     

巧用函数单调性解赛题

函数ｆ（ｘ）在区间［ａ,ｂ］上单调增加（或单调减少）,又ｃ、ｄ∈［ａ,ｂ］上,若ｆ（ｃ）＝ｆ（ａ）,则有ｃ＝ｄ．１　求代数式的值例１　已知ｘ、ｙ∈［－π４,π４］,ａ∈Ｒ,且　ｘ３＋ｓｉｎｘ－２ａ＝０４ｙ３＋ｓｉｎｙｃｏｓｙ＋ａ＝０则ｃｏｓ（ｘ＋２ｙ）＝　　．（１９９４年全国高中数学竞赛题）解　由已知条件,可得　　ｘ３＋ｓｉｎｘ＝２ａ（－２ｙ）３＋ｓｉｎ（－２ｙ）＝２ａ故可设函数ｆ（ｔ）＝ｔ３＋ｓｉｎｔ,则有ｆ（ｘ）＝ｆ（－２ｙ）＝２ａ．由于函数ｆ（ｔ）＝ｔ３＋ｓｉｎｔ,在［－π２,π２］上是单…     

求解不等式约束最优化问题的MBF—ODE方法

１引言考虑用基于修正内罚函数的常微分方程（ＭＢＦ－ＯＤＥ）方法求解下列不等式约束极小化问题：其中ｆi∈ｃ２：Ｒ,ｉ=0,１,…,ｍ．求解无约束极小化问题的ＯＤＥ的一般形式是其中,φ（ｘ）∈Ｃ１：ΩＲｎ→Ｒ;ｓ（ｘ）∈Ｃ１：ΩＲｎ→Ｒｎ且满足φ（ｘ）＞０,ｓＴ（ｘ）ｆ（ｘ）＜０,ｆ（ｘ）∈Ｃ１：Ｒｎ→Ｒ为目标函数．为便于用ＯＤＥ方法求解（１．ｌ）,可藉助于罚函数将（１．ｌ）变换为无约束极小化问题（见［７］．但由于经典罚函数（ＣＢＦ）在计算上有较大的困难,我们采用修正内罚函数（ＭＢＦ）．其基本思想是用…     

具有分段常数变元的时滞微分方程解的振动性(英文)

我们获得了带有分段常数变元的时滞微分方程ｘ′（ｔ）＋ａ（ｔ）ｘ（ｔ）＋∑ｍｉ＝１ｂｉ（ｔ）ｘ（［ｔ－ｉ］）＝０，ｔ≥０所有解振动的新的充分条件，这里［·］定义为最大整数函数．我们的结果改进了文献中的某些已知结果．     

滞后线性控制系统的输出能控性

本文对具有滞后的线性泛函微分方程所确定的滞后线性控制系统ｘ（ｔ）＝Ａ（ｔ）ｘ（ｔ）十Ｂ（ｔ）ｘ（ｔ－１）＋Ｃ（ｔ）ｕ（ｔ）ｔ∈（０，Ｔ］ｘ（ｔ）＝Φ（ｔ）ｔ∈［１，０］ｙ（ｔ）＝Ｄ（ｔ）ｘ（ｔ）＋Ｅ（ｔ）ｕ（ｔ）ｔ∈［－１，Ｔ］给出一些关于欧氏空间完全输出能控性的重要结论。并且对自治的滞后线性控制系统做了进一步研究，得到令人满意的充要条件；特别是通过与相应的常微分方程所确定的控制系统的输出能控性相比较，得到比较简明的判则。     

非对称不定问题的非协调多重网格法

１．引言设　是Ｒｄ（ｄ＝２;３）中的有界多角形区域,α是它的边界．考虑下列模型问题此处ｆ∈ＥＬ２（Ω）,系数ＡＥ（Ｃ１（Ω））ｄ×ｄ满足下列一致椭园条件此处α０是正常数．此外假设Ｂ∈（Ｃ１（Ω）ｄ和ｃ∈Ｃ０（Ω）（［１４］）．（１．１）式的变分形式是：找ｕ∈Ｈ０（Ω）使得最近,非对称不定问题的非协调多重网格法吸引了众多的研究,详见问,［７］;［１０］．考虑非协调元多重网格的一个重要原因是混合元和非协调元之间存在着紧密的联系（详见【几问,问）．设ＦＩ是ｆｉ拟一致的Ｈ角形或矩形剖分,是由连接Ｆ'－'（…     

变系数一阶中立型微分方程的振动性

考虑了微分方程［ｘ（ｔ）－ｐｘ（ｔ－τ）］′＋∑ｎｉ＝１Ｑｉ（ｔ）ｘ（ｔ－τｉ）＝０ｔ≥ｔ０（１）其Ｐ∈Ｒ＋＝［０,∞）,τ,τｉ为正常数,Ｑｉ（ｔ）∈Ｃ（［ｔ０,∞）,Ｒ＋）（ｉ＝１,２,…,ｎ）且∑ｎｉ＝１∫∞ｔ０Ｑｉ（ｔ）ｄｔ＝∞,获得了方程（１）振动的几个充分条件;减弱了文［１］Ｑ（ｔ）为周期系数的条件,推广和改进了文［１］的相应结果,并且有一些结果是新的     

脉冲中立型时滞微分方程解的振动性

本文讨论一阶脉冲中立型时滞微分方程［ｙ（ｔ）＋Ｐｙ（ｔ－σ）］′＋Ｑ（ｔ）ｙ（ｔ－σ）＝０，ｔ０，ｔ≠ｔｋ，ｋ＝１，２，…，ｙ（ｔ＋ｋ）－ｙ（ｔ－ｋ）＝ｂｋｙ（ｔｋ），ｋ＝１，２，…，｛（Ｅ）这里τ，σ，Ｐ均为常数，τ＞０，σ＞０，Ｑ（ｔ）∈Ｃ（［０，∞），Ｒ＋），ｂｋ＞－１，ｋ＝１，２，…．分三种情况，Ｐ－１；－１＜Ｐ＜０；Ｐ＞０给出了方程（Ｅ）所有解振动的充分条件．     

再生核空间偏微分方程解析数值解

１．引言 偏微分方程的近似解法一直是数值计算的重要内容之一。随着计算机的发展,各种实用的新方法也不断涌现．本文在再生核空间Ｈ　（Ｄ）中给出二阶偏微分方程边值问题解析形式的级数解,该级数解具有如下特点：１．级数截断就可直接得到解析数值解;２．解析数值解的误差在空间范数意义下单调下降． 设 Ｄ＝［ａ, ｂ］ ｘ ［ｃ, ｄ］是 Ｒ２中的任一矩形域, Г为边界,０,ｕ（ｘ,ｙ）∈Ｌ２（Ｄ）且是实的绝对连续函数,中规定内积如下： 范数定义为： 山中已证明码（利是一个再生核函数空间,其再生校函数研Ｘ,认（,…表达式…     

Convergence results for general linear methods on singular perturbation problems

Many numerical methods used to solve Ordinary Differential Equations, or Differential Algebraic Equations can be written as general linear methods. The B-convergence results for general linear methods are for algebraically stable methods, and therefore useless for nearly A-stable methods. The purpose of this paper is to show convergence for singular perturbation problems for the class of general linear methods without assuming A-stability.     

Fourth-Order Splitting Methods for Time-Dependant Differential Equations

This study was suggested by previous work on the simulation of evolution equations with scale-dependent processes,e.g.,wave-propagation or heat-transfer,that are modeled by wave equations or heat equations.Here,we study both parabolic and hyperbolic equations.We focus on ADI (alternating direction implicit) methods and LOD (locally one-dimensional) methods,which are standard splitting methods of lower order,e.g.second-order.Our aim is to develop higher-order ADI methods,which are performed by Richardson extrapolation,Crank-Nicolson methods and higher-order LOD methods,based on locally higher-order methods.We discuss the new theoretical results of the stability and consistency of the ADI methods.The main idea is to apply a higher- order time discretization and combine it with the ADI methods.We also discuss the dis- cretization and splitting methods for first-order and second-order evolution equations. The stability analysis is given for the ADI method for first-order time derivatives and for the LOD (locally one-dimensional) methods for second-order time derivatives.The higher-order methods are unconditionally stable.Some numerical experiments verify our results.     

Computation of Carlson's Multiple Hypergeometric Function R for Bayesian Applications

Abstract

Carlson's multiple hypergeometric functions arise in Bayesian inference, including methods for multinomial data with missing category distinctions and for local smoothing of histograms. To use these methods one needs to calculate Carlson functions and their ratios. We discuss properties of the functions and explore computational methods for them, including closed form methods, expansion methods, Laplace approximations, and Monte Carlo methods. Examples are given to illustrate and compare methods.     

一般线性方法的线性与非线性稳定性间的关系

１．引言１９６３年,Ｄａｈｌｑｕｉｓｔ以一类线性问题为模型提出了Ａ－稳定性概念,此后有关如何判断方法是否Ａ－稳定或确定其稳定域的研究十分活跃,袁兆鼎等~［１］中对此有详细的讨论．Ｂｕｒｒａｇｅ与Ｂｕｔｃｈｅｒ［２］以一类非线性问题为模型,就一般线性方法引入了代数稳定性概念．Ｂｕｔｃｈｅｒ［４］探讨了代数稳定性与Ａ－稳定性间的内在联系．为确保代数稳定性蕴涵Ａ－稳定性,Ｂｕｔｃｈｅｒ［５］进一步要求代数稳定性定义中涉及的矩阵Ｇ是正定的。然而这样一来,正如李寿佛［６］中指出的那样,许多ＡＮ稳定且按［４…     

常微分方程向前步组合离散化方法

一、一般理论 关于常微分方程组初值问题的数值求解,[1]首先提出:对方程组中各个微分方程采用不同的数值积分公式和不同的积分步长同时进行数值积分的思想.由这种思想构造的算法称为组合算法,在大系统的数字仿真等数值计算中得到了广泛的应用.国外正在发展的多速率算法或多帧速算法,是它的特例.由于并行处理机系统的迅速发展,这类算法将会得到更广泛的应用和进一步的研究.     

A new two-parameter family of nonlinear conjugate gradient methods

Conjugate gradient methods are an important class of methods for unconstrained optimization, especially for large-scale problems. Recently, they have been much studied. In this paper, we propose a new two-parameter family of conjugate gradient methods for unconstrained optimization. The two-parameter family of methods not only includes the already existing three practical nonlinear conjugate gradient methods, but has other family of conjugate gradient methods as subfamily. The two-parameter family of methods with the Wolfe line search is shown to ensure the descent property of each search direction. Some general convergence results are also established for the two-parameter family of methods. The numerical results show that this method is efficient for the given test problems. In addition, the methods related to this family are uniformly discussed.     

Expanding stability regions of explicit advective-diffusive finite difference methods by Jacobi preconditioning

Explicit time differencing methods for solving differential equations are advantageous in that they are easy to implement on a computer and are intrinsically very parallel. The disadvantage of explicit methods is the severe restrictions that are placed on stable time-step intervals. Stability bounds for explicit time differencing methods on advective–diffusive problems are generally determined by the diffusive part of the problem. These bounds are very small and implicit methods are used instead. The linear systems arising from these implicit methods are generally solved by iterative methods. In this article we develop a methodology for increasing the stability bounds of standard explicit finite differencing methods by combining explicit methods, implicit methods, and iterative methods in a novel way to generate new time-difference schemes, called preconditioned time-difference methods. A Jacobi preconditioned time differencing method is defined and analyzed for both diffusion and advection–diffusion equations. Several computational examples of both linear and nonlinear advective-diffusive problems are solved to demonstrate the accuracy and improved stability limits. © 1995 John Wiley & Sons, Inc.     

Constraint incorporation in optimization

Numerical methods for solving constrained optimization problems need to incorporate the constraints in a manner that satisfies essentially competing interests; the incorporation needs to be simple enough that the solution method is tractable, yet complex enough to ensure the validity of the ultimate solution. We introduce a framework for constraint incorporation that identifies a minimal acceptable level of complexity and defines two basic types of constraint incorporation which (with combinations) cover nearly all popular numerical methods for constrained optimization, including trust region methods, penalty methods, barrier methods, penalty-multiplier methods, and sequential quadratic programming methods. The broad application of our framework relies on addition and chain rules for constraint incorporation which we develop here.     

时滞积分微分方程的Rosenbrock方法

本文研究时滞积分微分方程的数值方法.通过改造现有常及离散型延迟微分方程的数值方法,并匹配以适当数值求积公式,构造了求解时滞积分微分方程的Rosenbrock方法,导出了其稳定性准则.数值例子阐明了所获方法的计算有效性.     

Interior-point methods for linear programming: a review

The paper reviews some recent advances in interior-point methods for linear programming and indicates directions in which future progress can be made. Most of the interior-point methods belong to any of three categories: affine-scaling methods, potential reduction methods and central path methods. These methods are discussed together with infeasible interior methods and homogeneous self-dual methods for linear programming. Also discussed are some theoretical issues in interior-point methods like dependence of complexity bounds on some non-traditional measures different from the input length L of the problem. Finally, the paper concludes with remarks on the comparison of interior-point methods with the simplex method based on their performance on NITLIB suite, a standard collection of test problems.