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1.
区间参数结构振动问题的矩阵摄动法   总被引:1,自引:1,他引:0  
当结构的参数具有不确定性时,结构的固有频率也将具有某种程度的不确定性.本文讨论了区间参数结构的振动问题,将区间参数结构的特征值问题归结为两个不同的特征值问题来求解.提出了求解区间参数结构振动问题的矩阵摄动方法.数值运算结果表明,本文所提出方法具有运算量小,结果精度高等优点.  相似文献   

2.
提出一种具有控制结构的向量均衡问题与向量映射的新的伪单调性概念,得到具有控制结构的向量均衡问题解的存在性及其解集的紧凸性.作为应用,得到具有控制结构的向量变分不等式与互补问题的解.  相似文献   

3.
崔登兰  李养成 《应用数学》2007,20(3):452-457
利用奇点理论中光滑映射芽的接触等价,研究状态变量和分歧参数均具有对称性的等变分歧问题,给出了状态变量具有D。对称性,分歧参数具有Z2对称性的等变分歧问题的两个识别条件.  相似文献   

4.
处理机具有不同开始加工时间的可中断排序问题   总被引:6,自引:0,他引:6  
本文对处理机具有的不同开始加工时间的可中断排序问题进行讨论,得到下面结论:若处理机具有相同开始加工时间的可中断排序问题存在最优排序算法,则相应的处理机具有不同开始加工时间的可中断排序问题也存在最优排序算法。  相似文献   

5.
复合材料拟周期结构的均匀化方法   总被引:10,自引:0,他引:10  
曹礼群  崔俊芝 《计算数学》1999,21(3):331-344
1.预备知识和问题的提出文山讨论了复合材料周期结构的数学问题,即复合材料弹性体的物理参数,几何参数具有某种周期拓扑结构的问题.但在实际问题中,有时还会遇到这些情形,由于受湿热环境和结构设计等因素的影响,弹性体不具有整体周期性,而是具有局部周期性,这就是本文要研究的拟周期性.数学上,这些问题可以表述为下列边值问题:其中fiCR”是有界区域,具有LIPschitz连续边界,A‘巾,旬,<二。‘x,八,k=l,…,n.是nXn阶矩阵,满足下列的A一条件.J.L.Lions(见文门)等曾对拟周期的二阶椭圆型边值问题进行了讨论,…  相似文献   

6.
臧振春 《数学季刊》2002,17(2):81-86
一些具有特殊结构的非线性规划问题我们已得到了很好的结果,本文研究一种具有特殊结构非线性规划问题的推广问题。  相似文献   

7.
杜乃杰  杜乃林 《数学杂志》2007,27(4):411-418
本文研究抽象变分问题(不必要求具有强制性)的Galerhin方法,利用泛函分析理论证明了:若变分问题的Galerkin逼近问题存在唯一解,那么它本身的解存在唯一且可由Galerhin逼近解无限逼近的充要条件是其Galerkin逼近格式具有某种稳定性.此结果是对Lax-Milgram定理和Cea定理的补充,可以应用于不必具有强制性的变分问题.  相似文献   

8.
讨论了任务具有优先约束的可中断不完全恒速机排序问题,若处理机具有不同开始加工时间的可中断排序问题存在最优算法,则相应的不完全恒速机排序问题也有最优算法。  相似文献   

9.
新课程改革的一个重要而具体的目标是倡导学生主动参与的探究式学习.问题是探究性学习的核心,没有问题便没有探究.探究的问题必须具有一定的难度但又让人能尝到果实,具有新颖性足以引发探究的问题,能够激发学生的探究欲望,激活学生的思维.经过以下四种问题探究式教学,笔者体会到学生的学习积极性高、课堂气氛活跃、教学效果明显. 一、重难点问题探究  相似文献   

10.
非线性反应扩散方程奇摄动问题   总被引:3,自引:1,他引:2       下载免费PDF全文
研究了具有非线性反应扩散方程奇摄动问题。在适当的条件下,利用微分不等式理论,讨论了当退化问题具有两个相交解时,原初始边值问题解的渐近性态。   相似文献   

11.
In the past decade, significant progress has been made in understanding problem complexity of discrete constraint problems. In contrast, little similar work has been done for constraint problems in the continuous domain. In this paper, we study the complexity of typical methods for non-linear constraint problems and present hybrid solvers with improved performance. To facilitate the empirical study, we propose a new test-case generator for generating non-linear constraint satisfaction problems (CSPs) and constrained optimization problems (COPs). The optimization methods tested include a sequential quadratic programming (SQP) method, a penalty method with a fixed penalty function, a penalty method with a sequence of penalty functions, and an augmented Lagrangian method. For hybrid solvers, we focus on the form that combines two or more optimization methods in sequence. In the experiments, we apply these methods to solve a series of continuous constraint problems with increasing constraint-to-variable ratios. The test problems include artificial benchmark problems from the test-case generator and problems derived from controlling a hyper-redundant modular manipulator. We obtain novel results on complexity phase transition phenomena of the various methods. Specifically, for constraint satisfaction problems, the SQP method is the best on weakly constrained problems, whereas the augmented Lagrangian method is the best on highly constrained ones. Although the static penalty method performs poorly by itself, by combining it with the SQP method, we show a hybrid solver that is significantly better than any of the individual methods on problems with moderate to large constraint-to-variable ratios. For constrained optimization problems, the hybrid solver obtains much better solutions than SQP, while spending comparable amount of time. In addition, the hybrid solver is flexible and can achieve good results on time-bounded applications by setting parameters according to the time limits.  相似文献   

12.
Infinite-dimensional optimization problems occur in various applications such as optimal control problems and parameter identification problems. If these problems are solved numerically the methods require a discretization which can be viewed as a perturbation of the data of the optimization problem. In this case the expected convergence behavior of the numerical method used to solve the problem does not only depend on the discretized problem but also on the original one. Algorithms which are analyzed include the gradient projection method, conditional gradient method, Newton's method and quasi-Newton methods for unconstrained and constrained problems with simple constraints.  相似文献   

13.
In this paper a numerical method is presented to solve singularly perturbed two points boundary value problems for second order ordinary differential equations consisting a discontinuous source term. First, in this method, an asymptotic expansion approximation of the solution of the boundary value problem is constructed using the basic ideas of a well known perturbation method WKB. Then some initial value problems and terminal value problems are constructed such that their solutions are the terms of this asymptotic expansion. These initial value problems are happened to be singularly perturbed problems and therefore fitted mesh method (Shishkin mesh) are used to solve these problems. Necessary error estimates are derived and examples provided to illustrate the method.  相似文献   

14.
The boundary contraction method is generalized in such a way that it is applicable to the Neumann and mixed boundary value problems over regions of irregular shape. Various variants of mixed boundary value problems can be solved numerically in a unified way with mesh points fewer than those required of ADI and SOR. The method is not iterative and therefore does not require the positive definiteness of eigenvalues which is the necessary condition of the stability of ADI and SOR. The method is also applicable to exterior problems. Thus the applicability of the contraction method to problems of practical importance is substantially improved.  相似文献   

15.
An approximate method of determining the critical loads in problems of the stability of compressed rods has been extended to statically indeterminate systems. For this purpose, a method has been developed for solving stability problems when there are extraneous unknowns defined by the stationarity condition for the potential energy of the system. It is shown that, combined with Grammel's method and Hamilton's variational principle, the method described for determining the extraneous unknowns in statically indeterminate systems can also be used in problems of finding the natural frequencies of vibrations of rods.  相似文献   

16.
Many real life problems can be modeled as nonlinear discrete optimization problems. Such problems often have multiple local minima and thus require global optimization methods. Due to high complexity of these problems, heuristic based global optimization techniques are usually required when solving large scale discrete optimization or mixed discrete optimization problems. One of the more recent global optimization tools is known as the discrete filled function method. Nine variations of the discrete filled function method in literature are identified and a review on theoretical properties of each method is given. Some of the most promising filled functions are tested on various benchmark problems. Numerical results are given for comparison.  相似文献   

17.
This paper investigates the analytical approximate solutions of third order three-point boundary value problems using reproducing kernel method. The solution obtained by using the method takes the form of a convergent series with easily computable components. However, the reproducing kernel method can not be used directly to solve third order three-point boundary value problems, since there is no method of obtaining reproducing kernel satisfying three-point boundary conditions. This paper presents a method for solving reproducing kernel satisfying three-point boundary conditions so that reproducing kernel method can be used to solve third order three-point boundary value problems. Results of numerical examples demonstrate that the method is quite accurate and efficient for singular second order three-point boundary value problems.  相似文献   

18.
In this paper, we use parametric quintic splines to derive some consistency relations which are then used to develop a numerical method for computing the solution of a system of fourth-order boundary-value problems associated with obstacle, unilateral, and contact problems. It is known that a class of variational inequalities related to contact problems in elastostatics can be characterized by a sequence of variational inequations, which are solved using some numerical method. Numerical evidence is presented to show the applicability and superiority of the new method over other collocation, finite difference, and spline methods.  相似文献   

19.
In this paper, we use a numerical method to solve boundary-value problems for a singularly-perturbed differential-difference equation of mixed type, i.e., containing both terms having a negative shift and terms having a positive shift. Similar boundary-value problems are associated with expected first exit time problems of the membrane potential in models for the neuron. The stability and convergence analysis of the method is given. The effect of a small shift on the boundary-layer solution is shown via numerical experiments. The numerical results for several test examples demonstrate the efficiency of the method.  相似文献   

20.
Huang  Na 《Numerical Algorithms》2020,85(4):1233-1254

In this work, we consider numerical methods for solving a class of block three-by-three saddle point problems, which arise from finite element methods for solving time-dependent Maxwell equations and a class of quadratic programs. We present a variant of Uzawa method with two variable parameters for the saddle point problems. These two parameters can be updated easily in each iteration, similar to the evaluation of the two iteration parameters in the conjugate gradient method. We show that the new iterative method converges to the unique solution of the saddle point problems under a reasonable condition. Numerical experiments highlighting the performance of the proposed method for problems are presented.

  相似文献   

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