统计模拟方法在优化经营管理中的应用

本文讨论经营管理中最佳配置的问题．利用统计模拟的方法和在讨论对象与已知分布之间建立对应关系，我们给出了一个实例的最优配置的解，并由此给出了我们的方法．     

结构振动诱导流场及附加质量的数值分析

将大型柔性结构低速振动诱导流体流场的问题, 归结为无粘性不可压缩无旋流动平面问题．在偶极子配置法基础上,发展了一种在结构和流体接触面上混合配置源汇和偶极子的奇点配置法,能够计算翼型、柱型等结构在流体中低速振动时诱导的流体流场并推导出流场的动能表达式,最终得到流体附加质量．给出了几个具有解析解的算例验证了此方法的可靠性．     

可压缩可混溶驱动问题的有限元配置法

多孔介质中可压缩可混溶驱动问题是非线性抛物系统,压力方程和饱和度方程用有限元配置方法来求解,证明了配置解的存在唯一性,最后得到了最优阶的误差估计．     

关于两点边值问题配置解的组合方法

目前,在用组合校正方法提高两点边值问题配置解的精度方面,已有一些工作。例如,Manabu Sakai考虑了三次样条配置解而采用两种不同投影的组合;黄友谦考虑了三次样条配置解同差分解的组合;林群,刘嘉荃给出了配置解的外推方法。本文基于上述工作的思想,提出一种新的组合方法。即通过对三次样条配置解和二次样条配置解进     

一阶广义分布参数系统的极点配置问题

本文讨论了一阶广义分布参数系统的极点配置问题,应用算子的广义逆给出了问题的解及解的构造性表达式．     

Urysohn方程数值解的一个高精度算法

Kumar和Sloan[1]及Atkinson,Flores[3]将配置法用于Hammerstein方程，并证明了在适当条件下近似解的迭代是超收敛的．这里针对于一般的vrysotri方程给出了一个近似解的迭代校正计算格式，证明了近似解不论是用什么方法求得的，在适当条件下迭代校正算法总具有超收敛性．将（1）     

一类二维对偶积分方程的解及其应用

二维对偶积分方程的理论与方法,在数学上尚未建立,因而完全的分析解不可能得到,从而使一些力学、物理与工程问题无法求解．利用双重展开和边界配置方法,得到了在数学和物理学上有着广泛应用的一类二维对偶积分方程的解答．把二维对偶积分方程化简成无限代数方程组,此方法的精确度取决于计算点的配置（即所谓边界配置）．通过对固体力学中某些复杂的初值-边值问题的应用说明此是方法有效的．     

用配置法解抛物型方程的误差估计

配置法可用来求各种类型方程的数值解。与Galerkin方法相比,它可避免计算数值积分。Douglas等人讨论了用配置法求抛物型方程初边值问题数值解的误差。本文讨论用配置法求具有间断系数抛物型方程数值解的误差。在求近似解时,允许系数的间断点与分割点不重合。在中Douglas用配置法求热传导方程的数值解,近似解空间由属于C~1(I)中的分段四次多项式全体组成,得到在分割结点处的误差有     

二阶广义系统的极点配置问题(英文)

以Ｈｉｌｂｅｒｔ空间算子理论为工具讨论二阶广义分布参数系统的极点配置问题,应用算子的广义逆给出了所讨论问题的解及解的构造性表达式．     

积分算子方程的连续型配置方法

1．引言由于对积分算子方程来说，配置法比Galerkin法具计算量小的优点（少算一重积分），故配置法更受人们重视．但已有的文献几乎都是将配置空间取作非连续的分片多项式样条空间，以得到某种超收敛结果（如［1，2］）．这种方法存在下列不足：（a）光滑核Volterra积分方程与光滑核Fredholm积分方程具完全不同的收敛性质［1］，且需用不同的方法获得其加速收敛结果（比较［31与［4］），尽管Volterra积分方程在理论上被看作是Fredholm积分方程的特殊情形；（b）光滑核Volterra积分方程的配置解不具任何超收敛性，其迭代配置解也只在结点…     

Interpolation correction for collocation solutions of Fredholm integro-differential equations

In this paper we discuss the collocation method for a large class of Fredholm linear integro-differential equations. It will be shown that, when a certain higher order interpolation operation is added to the collocation solution of this equation, the new approximations will, under suitable assumptions, admit a multiterm error expansion in even powers of the step-size . Based on this expansion, ideal multilevel correction results of this collocation solution are obtained.

     

An adaptive boundary collocation method for linear PDEs

The article proposes an adaptive algorithm based on a boundary collocation method for linear PDEs satisfying the maximal principle with possibly nonlinear boundary conditions. Given the error tolerance and an initial number of terms in the solution expansion, the algorithm computes expansion coefficients by collocation of boundary conditions and evaluates the maximum absolute error on the boundary. If error exceeds the error tolerance, additional expansion terms and boundary collocation points are added and the process repeated until the tolerance is satisfied. The performance of the algorithm is illustrated by an example of the potential flow past a cylinder placed between parallel walls. © 1995 John Wiley & Sons, Inc.     

A numerical approach for solving initial-boundary value problem describing the process of cooling of a semi-infinite body by radiation

In this article, we have introduced a Taylor collocation method, which is based on collocation method for solving initial-boundary value problem describing the process of cooling of a semi-infinite body by radiation. This method is based on first taking the truncated Taylor expansions of the solution function in the fractional differential equation and then substituting their matrix forms into the equation. Using collocation points, we have the system of nonlinear algebraic equation. Then, we solve the system of nonlinear algebraic equation using Maple 13 and we have the coefficients of Taylor expansion. In addition, numerical results are presented to demonstrate the effectiveness of the proposed method.     

一类弱奇性Volterra积分微分方程的级数展开数值解法

本文考察了一类弱奇性积分微分方程的级数展开数值解法,并给出了相应的收敛性分析.理论分析结果表明,若用已知函数的谱配置多项式逼近已知函数,那么方程的数值解以谱精度逼近方程的真解.数值实验数据也验证了这一理论分析结果.     

Analytical solution for the fully coupled static response of variable stiffness composite beams

An analytical solution is presented for the 3D static response of variable stiffness non-uniform composite beams. Based on Euler-Bernoulli theory, a set of governing differential equations are obtained, in which four degrees of freedom are fully coupled. For the variable stiffness beam, the governing field equations have variable coefficients reflecting the stiffness variation along the beam. Using the direct integration technique, the general analytical solution is derived in the integral form and the closed-form expressions of the obtained solutions are presented employing a series expansion approximation. The series expansion representation enables the proposed approach to be applicable for variable stiffness composite beams with arbitrary span-wise variation of properties. As an alternative solution, the Chebyshev collocation method is applied to the proposed formulation to verify the results obtained from the analytical solution. A number of variable stiffness composite beams made by fibre steering with various boundary conditions and stacking sequences are considered as the test cases. The static response are presented based on the analytical solution and Chebyshev collocation method and excellent agreement is observed for all test cases. The proposed model presents a reliable and efficient approach for capturing the complicated behaviour of variable stiffness non-uniform composite beams.     

Solution of a stochastic Darcy equation by polynomial chaos expansion

This paper deals with solving a boundary value problem for the Darcy equation with a random hydraulic conductivity field.We use an approach based on polynomial chaos expansion in a probability space of input data.We use a probabilistic collocation method to calculate the coefficients of the polynomial chaos expansion. The computational complexity of this algorithm is determined by the order of the polynomial chaos expansion and the number of terms in the Karhunen–Loève expansion. We calculate various Eulerian and Lagrangian statistical characteristics of the flow by the conventional Monte Carlo and probabilistic collocation methods. Our calculations show a significant advantage of the probabilistic collocation method over the directMonte Carlo algorithm.     

Full collocation methods for some boundary integral equations

In this paper we propose a fully discretized version of the collocation method applied to integral equations of the first kind with logarithmic kernel. After a stability and convergence analysis is given, we prove the existence of an asymptotic expansion of the error, which justifies the use of Richardson extrapolation. We further show how these expansions can be translated to a new expansion of potentials calculated with the numerical solution of a boundary integral equation such as those treated before. Some numerical experiments, confirming our theoretical results, are given. This revised version was published online in August 2006 with corrections to the Cover Date.     

A new collocation method for solution of mixed linear integro-differential-difference equations

Numerical solution of mixed linear integro-differential-difference equation is presented using Chebyshev collocation method. The aim of this article is to present an efficient numerical procedure for solving mixed linear integro-differential-difference equations. Our method depends mainly on a Chebyshev expansion approach. This method transforms mixed linear integro-differential-difference equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equation. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer algebraic system Maple10.