Wiener-Hopf积分方程的时序解法及其在平稳随机过程中的应用

在平稳随机过程的工程问题中,大多数问题可归纳为Wiener-Hopf积分方程的求解。本文提出求解Wiener-Hopf积分方程的一种时序解法及其在平稳随机过程中的应用。     

基于遗传算法的模糊关系方程求解

针对模糊关系方程的求解问题,即模糊综合评判逆问题,提出了一种基于遗传算法的求解方法.算法能有效地找出模糊关系方程的全局近似最优解,并且与模糊关系合成算子的具体形式无关,有良好的鲁棒性和自适应能力.仿真结果表明,此方法是一种有效、实用的模糊关系方程求解方法.     

一种改进的电场积分方程对天线辐射特性的研究

采用矩量法求解闭合结构的天线问题时可以使用混合场积分方程.然而实际运用中的一些天线常常是一部分结构属于开放结构,一部分结构属于闭合结构.对于这类问题,混合场积分方程并不能保证场解的唯一性,若使用电场积分方程来求解,则产生的阻抗矩阵性态差.因此,对于这类问题我们使用了一种改进的电场积分方程来求解,并用此种方法求解了天线的辐射方向图.文章中给出了算例,结果表明该方法是有效的.     

求解IETD问题的CFIE方程之比较

针对基于矩量法的积分方程时域求解存在的晚时震荡问题,分析两种稳定求解时域积分方程的混合场积分方程方法:隐式时间步进算法的混合场积分方程和基于拉盖尔多项式阶数步进算法的混合场积分方程。计算了目标的时域散射场和单站雷达散射截面,两种方法求得的结果吻合较好,表明两种方法解决时域积分方程晚时震荡问题的有效性。     

非线性电子电路方程解的一种快速收敛算法

本文以非线性电子电路的支路特性为基础,从电子元件的工作点出发,导出求解非线性电子电路方程的快速收敛算法,较好的解决非线性电子电路方程在求解过程中出现的振荡现象和假收敛问题.     

森林中电波传播的抛物方程法

抛物方程法能处理非均匀介质环境中的电波传播问题,并可用FFT步进算法快速求解,在电波传播中得到了广泛运用.该文用抛物方程法求解了森林中的电波传播问题,并将计算结果与Tamir侧面波模型的结果进行比较,二者吻合很好.最后用抛物方程法分析了森林中电波传播的特性.     

用线性函数空间理论求解标量波动方程和泊松方程的反演问题

基于线性函数空间理论的矩量法不仅适用于电磁场问题的数值计算,而且适用于解析法求解电磁场间题。本文分析了用本征函数作试函数和展开函数时的标量波动方程和泊松方程的反演形式,得到了一个很简单的对于各种边界条件普遍适用的公式。这一公式不仅适用于求解标量波动方程和泊松方程,而且只要稍加修改还可适用于解矢量波动方程问题,即求普遍形式的电磁场的激励问题。     

均匀随机媒质中传播的波有不同波数的m-n阶矩方程的解

在研究随机媒质中传播的波的一些有关问题时,常常需要求解波的矩方程。具有不同波数的m-n阶矩方程是一个抛物近似的偏微分波动方程。本文应用格林函数方法将偏微分方程变为积分方程,并用迭代法求得了该积分方程的解。同时,又应用接连散射的方法求解了具有不同波数的m-n阶矩方程,两种方法所得的结果完全相同。文中对解的物理含义作了说明,并讨论了用于波传播研究中的一些问题。     

均匀随机媒质中传播的波——有不同波数的m-n阶矩方程的解

在研究随机媒质中传播的波的一些有关问题时,常常需要求解波的矩方程。具有不同波数的m-n阶矩方程是一个抛物近似的偏微分波动方程。本文应用格林函数方法将偏微分方程变为积分方程,并用迭代法求得了该积分方程的解。同时,又应用接连散射的方法求解了具有不同波数的m-n阶矩方程,两种方法所得的结果完全相同。文中对解的物理含义作了说明,并讨论了用于波传播研究中的一些问题。     

电波传播中求解宽角抛物方程的误差分析

为求解不规则地形上电波以较大仰角传播问题,将波动方程近似转化为宽角抛物方程,并用分步付立叶变换方法求解。详细分析了这种求解方法产生误差的机理,给出了减小误差的方法,并以两种典型算例说明了误差的存在及其与计算时间的关系。     

High precision approximate analytical solutions to ODE using LS-SVM

The problem of solving differential equations and the properties of solutions have always been an important content of differential equation the study. In practical application and scientific research, it is difficult to obtain analytical solutions for most differential equations. In recent years, with the development of computer technology, some new intelligent algorithms have been used to solve differential equations. They overcomes the drawback of traditional methods and provide the approximate solution in closed form (i.e., continuous and differentiable). The least squares support vector machine (LS-SVM) has nice properties in solving differential equations. In order to further improve the accuracy of approximate analytical solutions and facilitative calculation, a novel method based on numerical methods and LS-SVM methods is presented to solve linear ordinary differential equations (ODEs). In our approach, a high precise of the numerical solution is added as a constraint to the nonlinear LS-SVM regression model, and the optimal parameters of the model are adjusted to minimize an appropriate error function. Finally, the approximate solution in closed form is obtained by solving a system of linear equations. The numerical experiments demonstrate that our proposed method can improve the accuracy of approximate solutions.     

On nonlinear fractional Klein-Gordon equation

Numerical methods are used to find exact solution for the nonlinear differential equations. In the last decades Iterative methods have been used for solving fractional differential equations. In this paper, the Homotopy perturbation method has been successively applied for finding approximate analytical solutions of the fractional nonlinear Klein-Gordon equation can be used as numerical algorithm. The behavior of solutions and the effects of different values of fractional order α are shown graphically. Some examples are given to show ability of the method for solving the fractional nonlinear equation.     

An efficient algorithm for solving Zakharov-Shabat inversescattering problem

An efficient numerical method for solving Zakharov-Shabat (ZS) inverse scattering problem is presented. In this method, instead of equivalent second-order differential equations to the Gel'fand-Levitan-Marchenko (GLM)-type integral equations, equivalent first-order differential equations are adopted and sufficiently accurate solutions to Zakharov-Shabat inverse problem can be achieved without iterations. Examples for applying it to design nonuniform transmission line (NTL) filters are also provided     

Real-time simulation of dynamic systems on systolic arrays

Systolic arrays have emerged as a powerful means for solving several computational problems of practical importance. This paper discusses the applicability of systolic arrays in the real-time simulation of dynamic systems. Systolic arrays are proposed for the simulation of dynamic systems which can be represented by a set of linear or nonlinear ordinary differential equations. Efficient techniques for solving the differential equations have been chosen in these systolic implementations, so that the real-time constraints can be satisfied, while maintaining both the stability and accuracy of the simulation. The complexity issues of the systolic implementations are also discussed. Conclusions are drawn regarding the efficiency and ease of using the systolic arrays, after comparison with the earlier solutions for this problem     

Two-dimensional analysis of semiconductor devices using general-purpose interactive PDE software

Analyzing currents and fields in VLSI devices requires solving three coupled nonlinear elliptic partial differential equations in two dimensions. Historically, these equations have been solved using a special-purpose program and batch runs on a large fast computer. We use a general-purpose program and interactive runs on a large minicomputer. We discuss the physical formulation of the semiconductor equations and give three example solutions: a short-channel MOSFET near punchthrough, a DMOS power transistor in the ON state, and a beveled p-n junction. These examples demonstrate that solutions to a very general class of semiconductor-device problems can be obtained using these methods.     

应用逆算子方法定量分析线性缓变p－n结

逆算子方法是一类新的求解强非线性问题的非数值方法．本文采用此类方法分析线性缓变ｐ－ｎ结．先把分析问题表述为一维非线性Ｐｏｉｓｓｏｎ方程，再应用逆算子方法求解该强非线性常微分方程，并采用Ｍａｔｈｅｍａｔｉｃａ软件推导其近似解析解，还对求得的近似解作了误差分析研究．模拟计算结果较为精确、可靠，基本上实现了线性缓变ｐ－ｎ结的定量分析，有助于更深入地定量研究ｐ－ｎ结的物理机理．此项研究表明，逆算子方法具有一定的优越性，它将为半导体器件的数值分析开辟一条新的途径．     

Stability Analysis of Periodic Orbits of Nonautonomous Piecewise-Linear Systems by Mapping Approach

In this brief, we present an exact stability analysis for periodic orbits of nonautonomous piecewise-linear systems. The described discrete-time maps are derived by connecting solutions at the switched points and solving relevant sets of linear differential equations. The coordinates of the switched points of the periodic orbit on each switching surface and the corresponding Jacobians are obtained. Theoretical analysis and simulation results for the piecewise-linear Duffing oscillator and Colpitts oscillator are presented to illustrate the proposed method.      

Formulas for the solutions of quadratic equations overGF(2^m)(Corresp.)

There are several known approaches to solving quadratic equations over GF(2^{m}). Here the approach to solving the equations is different from the known approaches in that the solutions are presented in terms of the parameters of the equations. The formulas for solving the quadratic equations are also used to solve the equations of degrees three and four. The results can be combined with other known techniques to solve equations of higher degrees.     

基于对称约化的偏微分方程相似解研究

由于非线性系统的复杂性,对于其求解问题的研究目前还没有通用的方法,为了丰富非线性系统的求解方法,在此通过偏微分方程的决定方程确定点对称无穷小生成元,结合对称约化中的非经典Lie群法得到热方程新的相似解,并基于符号计算系统Maple给出相应的符号计算方法和实现步骤。结果表明,该算法能够有效求解PDEs的相似解,并且不需要显示地求解对应于不变曲面条件的特征方程,同时也适用于其他的发展方程。