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给出并证明了薛定谔方程中高斯包络孤子的表达式.针对该高斯包络孤子进一步提出了薛定谔方程中存在高斯包络孤子相互作用的情况;针对薛定谔方程提出其辛算法.通过分离波函数实部和虚部把薛定谔方程变换成标准的哈密顿正则方程组,对正则方程进行欧拉中心差分离散实现辛算法.给出了辛算法的守恒量,并证明了其稳定性.对薛定谔方程中的高斯包络孤子运动及多孤子相互作用过程进行了数值仿真,实验结果证明了所提观点的正确性及辛算法的有效性. 相似文献
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为了加深对于矢量拉普拉斯算符的理解,本文选择直角坐标系,从矢量的双旋度出发,详细推导了矢量拉普拉斯算符的解析表达式,即等于矢量梯度的散度减去双旋度,然后分析了其在矢量磁位泊松方程化简过程中的应用,最后在此基础上推导了圆柱坐标和球坐标系下矢量拉普拉斯算符的表达式. 相似文献
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通过变量代换平滑三角形上推迟位(标量位函数和矢量位函数)并消除推迟矢量位旋度的奇异性,使得采用数值积分法就能够精确快速地计算任意正则时间基函数与推迟位函数及推迟矢量位旋度之间的时间卷积运算,可用于基于任意类型时间基函数的时域电场、时域磁场及其混合场积分方程时间步进(MOT )算法。与时间卷积运算的解析法对比分析表明,该时间卷积数值积分方法能够精确快速地计算基于任意类型时间基函数和不同时间步长条件下时域积分方程MOT算法的阻抗矩阵元素;而具体的计算实例也表明,阻抗矩阵的精确计算显著地提升了时域积分方程MOT算法的后时稳定性和求解精度。 相似文献
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一维逆散射问题的数值解法及近似解法 总被引:3,自引:1,他引:2
一维逆散射问题,本世纪中期已归结为求解Gel'fand-Levitan积分方程的问题,其在某些情况下的解析解已经获得。本文研究两种不同的方法。其一为迭代蛙跃法,即用数值方法求解积分方程。实际计算表明,此法简明而有效。另一为Born近似方法,它给出了解析表达式,由此可重建分界面附近一定区域的势函数。文中用这两种方法讨论了若干例子。 相似文献
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我们对"电磁场"课程采取了课前作业的教学方法。该方法是将下节课知识点所用到的相关数学、物理概念和公式通过作业的方式提前布置给学生。本文以分离变量法和达朗贝尔方程的求解为例说明该方法的实施。该两例将有关方程的求解分解为已经学过的数个方程,作为作业预先布置给学生。这种教学方法已收到了良好的教学效果。 相似文献
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S. P. Skobelev 《Journal of Communications Technology and Electronics》2007,52(3):304-312
The method proposed for solution of 2D problems is extended to solution of a 3D problem for an array of circular waveguides with protruding cylinder-conical dielectric rods. The transverse electromagnetic field in the domain containing the rods is expanded into a series of vector functions of a Floquet channel. The series contains variable coefficients whose values are determined from solution of a system of ordinary differential equations derived upon projection of the Maxwell equations onto the same vector functions. The differential equations are transformed into algebraic equations via application of a 1D finite-element method and matching of fields with waveguide and spatial harmonics on the boundaries of this domain. The results of numerical solution of the obtained algebraic system are used for calculation of the array characteristics, which are compared to the data published in the literature and the experimental results available for several particular cases. 相似文献
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Zhou Zongfang 《中国邮电高校学报(英文版)》1994,(1)
1IntrodutionIn[IJlanewmethodispresentedforfindingthelocaloptimaofthegeneralconstrainedoptimization.Thediscussionabouttheconstraintsiscontinuedbytheordinarydifferentialequationsinsection2.Itisprovedthatthesolutionsstartingfromtheneighbourhoodofacriticalpoi… 相似文献
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Solution methods for transient and dynamic stability 总被引:2,自引:0,他引:2
The transient stability study is used to examine the dynamic behavior of a power system following a disturbance. Transient stability programs have grown in the size of the power system under study, in the duration of the study, and in the magnitude of the disturbance. Each prime mover is represented by as few as two or as many as forty ordinary differential equations. These equations are coupled to a set of algebraic equations (two per node) which describe the network. Available programs frequently use explicit fixed step integration methods and the sequential solution of the differential and algebraic equations. Recent advances in solution methods have been directed toward implicit integration techniques and the simultaneous solution of the whole set of differential-algebraic equations. The transient stability problem, the unit models currently in use, and recent advances in solution methods are briefly reviewed. A dynamic stability program is described which incorporates comprehensive dynamic models of prime movers; the results of several experiments using this program are presented. 相似文献
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麦克斯韦方程组是描述宏观电磁现象普遍规律的基本方程,给出恰当的定解条件才能确保麦克斯韦方程组有解且唯一。本文从确定矢量场唯一解的亥姆霍兹定理出发,提出电磁场基本方程的构成,并基于时变电磁场和静态电磁场的特性给出定解条件。这为各种电磁场问题求解方法提供了依据,也为解的正确性提供了判据。 相似文献
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针对分数阶动态电路,基于分数阶微分方程的解析解,研究0~2阶分数阶动态电路的阶跃响应.利用MATLAB软件,得到不同阶次分数阶电路的阶跃响应曲线,并与整数一阶电路和二阶电路的阶跃响应作了对比研究,为今后分数阶电路的研究奠定了基础. 相似文献
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Area-time upper bounds for the iterative solution of linear systems and for the inversion of matrices in VLSI models are obtained and compared to the known upper bounds obtained by direct methods. Error analysis gives the number of iterations for which an acceptable error bound is obtained in the result. The use of the Jacobi method to solve partial differential equations is discussed. 相似文献
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通过两个步骤,构造了Generalized Zakharov-Kuzentsov方程的无穷序列类孤子新解. 第一步、利用首次积分与函数变换,把一种非线性常微分方程转化为几种常用的辅助方程,并获得了几种常用辅助方程的新解、B\"{a}cklund变换和解的非线性叠加公式. 第二步、借助一系列的变换与符号计算系统~Mathematica,构造了Generalized Zakharov-Kuzentsov方程的无穷序列类孤子新解. 相似文献
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习友宝 《电气电子教学学报》2011,(6):109-111
本文讨论了当前一阶电路暂态过程及时间常数的相关教学中存在的问题。文章以典型的RC阻容分压器电路和两个一阶电路-RC与RL的组合电路为例,说明电路阶数的判断及时间常数的求取,给出了直流一阶电路微分方程的通式,其解即为三要素法表达式,并列出了几个应用实例。 相似文献