机电系统的尼尔森方程

本文给出了一种对机电系统进行分析建模的新方法,即机电系统尼尔森方程.通过机电系统的尼尔森方程对机电系统进行分析和建模与利用拉格朗日方程对机电系统进行建模具有相同的作用.根据方程求导方式的不同可知,在一些情况下,使用尼尔森方程建模比使用拉格朗日方程可能会容易些.在本文中给出机电系统尼尔森方程的推导过程并通过实例对尼尔森方程的使用加以说明.     

Burgers方程的精确孤立波解的符号计算

借助于符号计算Maple,给出了一种构造非线性波动方程行波解的直接代数方法,该方法的主要特点是充分利用Riccati方程.使用此方法得到Burgers方程的多组精确行波解,其中包括一些新的孤立波解,这种方法也适用于求解其它的非线性波动方程（组）.     

非线性演化方程的新Jacobi椭圆函数解

基于sinh-Gordon方程的椭圆函数解,构造新的试探解来扩展sinh-Gordon方程展开法.利用该方法研究了KdV-mKdV方程,双sine-Gordon方程和BBM方程,获得了这些方程的新Jacobi椭圆函数解.该方法也能用来求解其他数学物理中的非线性演化方程.     

关于一般耦合矩阵方程的迭代对称解

本文构造了一个有效的迭代方法(CGL)去求解一般耦合矩阵方程的对称解.若一般耦合矩阵方程关于对称解相容,则对于任意给定的初始对称矩阵组,利用所构造的迭代算法,都能在有限步迭代出所求问题的一组对称解,若选用一些特殊的初值,则可获得矩阵方程的极小范数对称解.最后的数值例子表明了所给算法的有效性.     

一些特殊方程的计算机程序解法

在人们生产、生活、以及科学研究中,常常会出现一些不容易求解的非线性方程或非线性方程组等特殊方程。文章运用数学知识和计算机MATLAB语言,介绍了这些方程的求解,从而快速得到这些方程的解。     

指数函数方法及其在非线性发展方程中的应用

在求解非线性发展方程时,指数函数方法是一种非常简洁有效的方法。用此方法求解了2+1维Burgers方程和2+1维KP方程,并且得到了一些新的精确解。     

求解规范型Lyapunov矩阵方程的新方法

本文揭示了规范型Lyapunov矩阵方程及其对偶方程的一些特殊性质,充分压缩解矩阵的未知元素,并利用对偶解矩阵与解矩阵的合同关系,提出了一种高精度、高效率求解规范型Lyapunov方程的新算法,文中举例验证了新算法的正确性。 Lyapunov矩阵方程 能控制和能观测规范型 单输入单输出系统     

解耦的声表面波波动方程的求解􀀂

由于压电材料对称性的存在,当一些压电材料取某些特殊切型时,声表面波存在着解耦现象,解耦波常有几种固定的模式.本文对解耦的声表面波波动方程的求解进行了研究.并以PZT-5H材料为例,用编制的程序对解耦的纯Rayleigh波和B-G波进行了计算机数值求解,其结果与文献[3]的值一致.说明这一求解原理和方法普遍适用于对各种解耦的声表面波波动方程的求解.对于全面分析SAW的传播特性具有一定的参考价值.     

一种通过求解程序方程进行程序转换的方法

在程序展开的理论基础上,本文提出了一种通过求解程序方程来进行程序转换的方法。首先,程序转换的目标表示为程序方程。虽然这样的方程通常是高度复杂而难以直接求解的,但是,通过程序的正交展开,可以将其化为简单方程组。最后,简单方程的解可由方程化简与求解的一组公式以及程序代数定律形式地导出。本文着重讨论了方程的化简和求解,并给出了一些转换实例。     

广义Fitzhugh Nagumo方程的无穷序列新解

利用辅助方程的几种结论,构造了广义Fitzhugh-Nagumo方程的多种无穷序列新解.步骤一,利用函数变换与首次积分,给出了辅助方程的新解、Bcklund变换和解的非线性叠加公式.步骤二,通过函数变换,将广义Fitzhugh-Nagumo方程的求解问题转化为非线性常微分方程的求解问题.步骤三,利用符号计算系统Mathematica与辅助方程的几种结论,构造了广义Fitzhugh-Nagumo方程的多种无穷序列新解.     

用参数法求一些特殊的线性代数方程组的数值解

本文将求解线性方程组数值解的双参数法进行推广,得到(?)种求解一些特殊的线性方程组的较为(?)般的方法-参数法,并具体给出利用三组参数求解拟二对角方程组和拟Hessen-berg方程组的算法.此算法具有明显的优越性.比如,在求解拟二对角方程组时,和利用LU分解法相比,乘除运算的次数由11n-16变为9n+20,所需要设定的向量组由5个降为4个.在求解拟Hessenberg方程组时,和Gauss消去法相比,除法运算的次数由1/2n(n+1)变为3n-4.这对求解大型的拟三对角方程组和拟Hessenberg方程组非常有利.当然,此种方法还可以用来求解其它一些方程组。     

Delay dependent estimates for waveform relaxation methods for neutral differential-functional systems

In this paper, the problem of delay dependent error estimates for waveform relaxation methods applied to Volterra type systems of functional-differential equations of neutral type including systems of differential-algebraic equations is discussed. Under a Lipschitz condition (with delay dependent right-hand side) imposed on the so-called splitting function it is shown how the error estimates depend on the character of delays and that for this reason they are better than the known error estimates for relaxation methods. It is proved that under some assumptions the exact solution can be obtained after a finite number of steps of the iterative process, i.e., we prove that the waveform relaxation methods have the same property as the classical method of steps for solving delay-differential equations with nonvanishing delays. We also show the convergence of the waveform relaxation method without assuming that the spectral radius of the corresponding matrix related to the Lipschitz coefficients for the neutral argument is less than one.     

Generalized newton multi-step iterative methods GMNp,m for solving system of nonlinear equations

A generalization of the Newton multi-step iterative method is presented, in the form of distinct families of methods depending on proper parameters. The proposed generalization of the Newton multi-step consists of two parts, namely the base method and the multi-step part. The multi-step part requires a single evaluation of function per step. During the multi-step phase, we have to solve systems of linear equations whose coefficient matrix is the Jacobian evaluated at the initial guess. The direct inversion of the Jacobian it is an expensive operation, and hence, for moderately large systems, the lower-upper triangular factorization (LU) is a reasonable choice. Once we have the LU factors of the Jacobian, starting from the base method, we only solve systems of lower and upper triangular matrices that are in fact computationally economical. The developed families involve unknown parameters, and we are interested in setting them with the goal of maximizing the convergence order of the global method. Few families are investigated in some detail. The validity and numerical accuracy of the solution of the system of nonlinear equations are presented via numerical simulations, also involving examples coming from standard approximations of ordinary differential and partial differential nonlinear equations. The obtained results show the efficiency of constructed iterative methods, under the assumption of smoothness of the nonlinear function.     

基于整数方程的逻辑方程组求解方法研究

为快速有效地求解大量逻辑方程组,根据逻辑运算的特点详细阐述了将逻辑方程转化成等效整数方程的原理和方法,并对得到的整数方程进行化简,提出了整数方程组的一般求解方法,即吴方法和Grobner基理论。接着给出并完善了一种基于快速多项式乘法的消元法,大大降低了求解的复杂度,最后将基于整数方程的逻辑方程组求解方法应用于故障诊断,并举例验证。     

On the Equations of Kinematics and Dynamics of Constrained Mechanical Systems

The method of constructing of kinematical and dynamicalequations of mechanical systems, applied to numerical realization, isproposed in this paper. The corresponding difference equations, whichare obtained, give a guarantee of computations with given precision. Theequations of programmed constraints and those of constraintperturbations are defined. The stability of the programmed manifold fornumerical solutions of the kinematical and dynamical equations isobtained by means of corresponding construction of the constraintperturbation equations. The dynamical equations of system withprogrammed constraints are set up in the form of Lagrange equations ingeneralized coordinates. Certain inverse problems of rigid body dynamicsare considered.     

Noncentered schemes and schock propagation problems

In this paper, the noncentered difference scheme given by Mac Cormack for the numerical solution of the gas dynamics equations is studied from a theoretical point of view, and its computational properties are tested for shock propagation problems. By means of a nonlinear analysis for a scalar equation, it is shown why there is no oscillations in the shock profile when the directions of the differences are correctly chosen. Computations are made for the propagation of a shock wave in a channel and along a curve wall. The results are compared to those given by Whitham's theory.     

Nonminimal Kane's Equations of Motion for Multibody Dynamical Systems Subject to Nonlinear Nonholonomic Constraints

Nonholonomic constraint equations that are nonlinear in velocities are incorporated with Kane's dynamical equations by utilizing the acceleration form of constraints, resulting in Kane's nonminimal equations of motion, i.e. the equations that involve the full set of generalized accelerations. Together with the kinematical differential equations, these equations form a state-space model that is full-order, separated in the derivatives of the states, and involves no Lagrange multipliers. The method is illustrated by using it to obtain nonminimal equations of motion for the classical Appell–Hamel problem when the constraints are modeled as nonlinear in the velocities. It is shown that this fictitious nonlinearity has a predominant effect on the numerical stability of the dynamical equations, and hence it is possible to use it for improving the accuracy of simulations. Another issue is the dynamics of constraint violations caused by integration errors due to enforcing a differentiated form of the constraint equations. To solve this problem, the acceleration form of the constraint equations is augmented with constraint stabilization terms before using it with the dynamical equations. The procedure is illustrated by stabilizing the constraint equations for a holonomically constrained particle in the gravitational field.     

Discretization error due to the identity operator in surface integral equations

We consider the accuracy of surface integral equations for the solution of scattering and radiation problems in electromagnetics. In numerical solutions, second-kind integral equations involving well-tested identity operators are preferable for efficiency, because they produce diagonally-dominant matrix equations that can be solved easily with iterative methods. However, the existence of the well-tested identity operators leads to inaccurate results, especially when the equations are discretized with low-order basis functions, such as the Rao-Wilton-Glisson functions. By performing a computational experiment based on the nonradiating property of the tangential incident fields on arbitrary surfaces, we show that the discretization error of the identity operator is a major error source that contaminates the accuracy of the second-kind integral equations significantly.     

Solving applied general equilibrium models represented as a mixture of linearized and levels equations

General equilibrium moels are usually represented as a system of levels equations (e.g., in North America) or a system of linearized equations (e.g., in Australia). Either representation can be used to obtain accurate solutions. General-purpose software is available in both cases-GAMS or MPS/GE is typically used by levels modellers and GEMPACK by linearizers. Some equations (notably accounting identities) are naturally expressed in the levels while others (especially behavioural equations) are naturally expressed in a linearized form. This paper describes the new GEMPACK facility for solving models represented as a mixture of levels and linearized equations and discusses the advantages to modellers of using such a representation.     

Social influences related to college students’ use of Macintosh computers on an all-PC campus

In the present qualitative research study, 35 Mac users were interviewed in a university campus that exclusively supports PC machines. We particularly explored the Mac-users’ social influences, saving technological and other influences for future reports. Results showed Mac users to possess significant connections with other Mac users on the university campus. The Mac users in our study indicated that positive, past exposure, including Apple’s advertising of Macs, had sharp influences on their decisions to become and remain Mac users.