Chebyshev polynomial solutions of systems of higher-order linear Fredholm-Volterra integro-differential equations

A Chebyshev collocation method, an expansion method, has been proposed in order to solve the systems of higher-order linear integro-differential equations. This method transforms the IDE system and the given conditions into the matrix equations via Chebyshev collocation points. By merging these results, a new system which corresponds to a system of linear algebraic equations is obtained. The solution of this system yields the Chebyshev coefficients of the solution function. Some numerical results are also given to illustrate the efficiency of the method. Moreover, this method is valid for the systems of differential and integral equations.     

Sliding mode control of manipulators using first-order equations of motion with diagonal mass matrix

This paper presents a proposition of a sliding mode controller for a rigid manipulator expressed in terms of the generalized velocity components (GVC) vector. Introduction of GVC (Trans. ASME J. Appl. Mech. 62 (1995) 216) together with generalized positions leads to two first-order decoupled equations of motion instead of a single second-order equation. It is shown that the new controller, stable in the sense of Lyapunov, has different properties and can, according to Slotine and Li (Int. J. Robotics Res. 6 (1987) 49), give better performance than the classical sliding mode controller. Both control algorithms were tested on a 3 d.o.f., 3-D Yasukawa-like robot.     

某些类具有Hilbert核奇异积分的卷积型方程

利用离散的Fourier变换首次讨论了含有H ilbert核和卷积核的若干类奇异积分方程的求解,并首先在L2[-aπ2,aπ2](a>0)上得到了可解条件和一般解。     

一类二阶泛函微分方程的周期

采用更精确的先验估计,利用重合度理论讨论了一类二阶泛函微分方程的周期解,得到了该方程存在2周期解的充分条件,改进了相关文献中的定理。     

具有分段常数超前变元微分方程的振动性

本文讨论了一类具有分段常数超前变元微分方程解的表示及其振动性。     

一类脉冲中立型抛物方程解的强迫振动性

讨论了一类具有连续分布滞量的脉冲中立型抛物方程解的强迫振动性，利用微分不等式方法将所讨论的脉冲中立型偏微分方程转化为脉冲中立型时滞微分方程的问题，获得了其一切解振动的充分性判据；将脉冲中立型微分方程的振动性质推广到具时滞的脉冲中立型偏微分方程．     

一阶具连续变量中立型差分方程解的振动性

借助研究时滞微分方程振动性的一般方法 ,建立了一阶具连续变量中立型差分方程Δ[x(t) -p(t)x(t-τ) ]+q(t)x(t-σ) =0解的的振动性的充分条件 ,其中τ,σ为正常数 ,p ,q∈C(R+,R+) ,Δ指步长为τ的向前差分算子 .     

非线性差分方程守恒律计算的算法

本文给出了非线性差分方程守恒律计算的算法，利用此算法可计算出离散KdV方程的守恒律。     

Using the United States Census Data to Introduce Differential Equations

Abstract

This article describes a method for using the United States Census data to open a differential equations course. The question of finding a model for the United States population data gives students a first experience with creating a model using differential equations, and also understanding derivatives, what they mean, and how to calculate them in the context of real data. This model-building start motivates further exploration in many of the standard differential equations topics: the method of separation of variables, slope fields, autonomous equations, equilibria, and stability.     

两种电磁场边界条件推导之比较

在对电力，电子、微波、通讯等专业的学习中，对电磁场的分析是一个非常重要的部分．它不仅要求对该条件的知识有个全面的了解，而且也要求熟练应用麦克斯韦方程推导相应的边界条件，而另外一种切实可行的方法则是应用斯托克原理及麦克斯韦方程进行综合分析，并且可将过程一定的简化。