共查询到20条相似文献，搜索用时 375 毫秒
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在1996 年，C. Krattenthaler 给出了一个能够统一大部分的矩阵反演的通用的矩阵反演公式 并利用这个公式导出了很多新的超几何级数型求和公式，但是其证明非常复杂。本文给出这个反演公式的一个初等证明。 相似文献
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分期付款是现代人生活中的一个普遍现象，但是由于其涉及面广、概念多、内容复杂，特别是其数学模型比较烦杂，因此其实际的算法对于大多数普通消费者来说都是很难掌握和理解的，只能根据银行给予的利率表和计算公式进行运算，但是公式是如何得到的，对消费者是否公平，是否存在银行采用复利的计算方法，一般人都无从知晓，本文就分期付款中还款公式的由来和其由复利变单利的运算思想给予了一定的说明和推导。 相似文献
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数学公式是科技文档不可或缺的重要组成部分，具有复杂的二维结构和嵌套结构。数学文档有多种格式，包括word、PDF、MathMI、Tex＼LaTex等，如何对文档中的公式进行检索，如何判定两个公式匹配则成为一个难题。公式匹配包括精确匹配、语义匹配和结构匹配等，如果简单地使用字符串匹配技术，则无法实现公式的匹配，因此必须针对教学公式特点，研究出相应公式匹配方法。首先对文档进行归一化，然后对公式进行匹配。如果有多个文档或网络检索的话，则为了加快速度，需要构建索引等结构。 相似文献
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有一些同学物理总学不好，纠其原因就是学习粗枝大叶，认为物理就是记住公式，多做习题，但是这些还是远远不够的。 相似文献
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利用最优化思想，根据一阶常微分方程数值解的收敛性和稳定性，引进最优化技术，确定最优系数，得到强稳定的线性三步和四步公式以及三阶Runge-Kutta最优算法，经地实际计算，部分公式的结果优于目前已有的公式。 相似文献
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<正>高中数学中三角函数诱导公式比较多，学生很容易混淆。如果单靠死记硬背是不能够获得好的学习效果，也极容易造成遗忘及错记的。本文在原有教参的基础上归纳总结出一种诱导公式的记忆方法，兼顾学习如何推导出公式，也可直接运用结论公式的方法。一旦遗忘公式，依照此法可以立马推出所需结论。 相似文献
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范建东 《内蒙古科技与经济》2000,(Z1)
公式是构成物理知识的重要组成部分 ,正确地理解、掌握物理公式是学好物理的基础。目前 ,在公式的教学中存在的主要问题是 :对公式教学应达到的目的不明确 ,忽视公式建立的条件和背景 ,断头去尾、取其表而略其质 ;忽视公式间的相互联系 ,把公式孤立起来 ,这种教法的结果 ,使学生对公式只会死记硬背 ,不能正确理解和灵活应用。笔者从多年的教学实践中体会到 ,要让学生理解、掌握和灵活应用物理公式 ,教师在授课时 ,应注意以下几个问题 :1 注意公式中各个物理量的含义、单位和取号1.1 注意公式中各个物理量的确切含义物理公式是由表示一定物… 相似文献
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In this paper, the Bagley-Torvik equation, which has an important role in fractional calculus, is solved by generalizing the Taylor collocation method. The proposed method has a new algorithm for solving fractional differential equations. This new method has many advantages over variety of numerical approximations for solving fractional differential equations. To assess the effectiveness and preciseness of the method, results are compared with other numerical approaches. Since the Bagley-Torvik equation represents a general form of the fractional problems, its solution can give many ideas about the solution of similar problems in fractional differential equations. 相似文献
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A numerical method is proposed for solving multi-dimensional hyperbolic–parabolic differential equations with the nonlocal boundary condition in t and Dirichlet and Neumann conditions in space variables. The first and second order of accuracy difference schemes are presented. The stability estimates for the solution and its first and second orders difference derivatives are established. A procedure of modified Gauss elimination method is used for solving these difference schemes in the case of a one-dimensional hyperbolic–parabolic differential equations with variable coefficients in x and two-dimensional hyperbolic–parabolic equation. 相似文献
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Moving mesh partial differential equations have been widely used in the last decade for solving differential equations exhibiting large solution variations such as shock waves and boundary layers.In this paper, we have applied a dynamic adaptive method for solving time-dependent differential equations. The mesh velocities are governed by an equation in which a relaxation time is employed to move nodes in such a way that they remain concentrated in regions of rapid variation of the solution. A numerical example involving a blow-up problem shows the advantage of using a variable relaxation time over a fixed one. 相似文献
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Optimal parametrization in numerical construction of curve 总被引：1，自引：0，他引：1
E.B. Kuznetsov 《Journal of The Franklin Institute》2007,344(5):658-671
The application of the optimal parametric continuation method to constructing a solution set curve for a system of nonlinear algebraic or transcendental equations depending on a parameter is considered. There are discussed two approaches to solving this problem—the use of iterative methods and reduction to an initial value problem for a system of ordinary differential equations. The algorithm suggested in this paper can also be used for finding an appropriate initial approximation when solving a system of nonlinear algebraic or transcendental equations not depending on a parameter by an iterative method. 相似文献
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Nonlinear two-point boundary value problems have always been difficult to solve. The difficulty is compounded if the problem tends to be inherently unstable. This paper describes an algorithm for solving such sensitive boundary value problems. The procedure is based on a computational method for finding the general solution of systems of ordinary differential equations used in conjunction with the multi-point quasilinearization method of Miele. The method is demonstrated by solving Troesch's problem and a singular perturbation problem. 相似文献
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An improvement of the Peano-Baker iterative method (matrizant method) for solving a system of first order linear differential equations with variable coefficients is presented. The new method utilizes the structure of the matrix of coefficients to define iterative schemes which may converge much more rapidly than the traditional method. 相似文献
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《Journal of The Franklin Institute》2021,358(16):8639-8655
Interconnection and damping assignment passivity-based control scheme has been used to stabilize many physical systems such as underactuated mechanical systems through total energy shaping. In this method, some partial differential equations (PDEs) related to kinetic and potential energy shaping shall be solved analytically. Finding a suitable desired inertia matrix as the solution of nonlinear PDEs relevant to kinetic energy shaping is a challenging problem. In this paper, a systematic approach to solving this matching equation for systems with one degree of underactuation is proposed. A special structure for desired inertia matrix is proposed to simplify the solution of the corresponding PDE. It is shown that the proposed method is more general than that of some reported methods in the literature. In order to derive a suitable desired inertia matrix, a necessary condition is also derived. The proposed method is applied to three examples, including pendubot, VTOL aircraft, and 2D SpiderCrane. 相似文献
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There are few techniques available to numerically solve linear Fredholm integrodifferential-difference equation of high-order. In this paper we show that the Taylor matrix method is a very effective tool in numerically solving such problems. This method transforms the equation and the given conditions into the matrix equations. By merging these results, a new matrix equation which corresponds to a system of linear algebraic equation is obtained. The solution of this system yields the Taylor 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 differential, difference, differential-difference and Fredholm integral equations. In some numerical examples, MAPLE modules are designed for the purpose of testing and using the method. 相似文献
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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. 相似文献
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A numerical method for solving the higher order linear difference equations with variable coefficients and mixed argument under the mixed conditions is presented. The method is based on the hybrid Legendre and Taylor polynomials. The solution is obtained in terms of Legendre polynomials. IIIustrative examples are included to demonstrate the validity and applicability of the technique. 相似文献