共查询到20条相似文献,搜索用时 125 毫秒
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快速造P(n,k)大表的左肩法则和斜线法则 总被引:10,自引:0,他引:10
设P(n,k)为整数n分为k部的无序分拆的个数,每个分部≥1,它为大师欧拉所建立(1707-1783).它是组合图论和数论里最重要的数据之一.然而,它却十分难于计数和造表.本文,由公式P(n,k)=P(n-1,k-1)+P(n-k,k)定义了P(n,k)的左肩数和锐角数,并由此得到求P(n,k)的左肩法则(第一法则).还根据本文作者[5]的一些重要定理得到求 P(n,k)的斜线法则(第二法则).使用这些法则得到造P(n,k)大表的有趣原理.为方便计,我们仅用第一法则设计了计算机程序,用此程序即可快速造出任意大的P(n,k)表. 相似文献
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本文研究了圆周上带希尔伯特核的柯西奇异积分的复合梯型公式.利用连续的分片线性函数逼近被积函数,得到积分公式的误差估计;然后用积分公式构造求解对应奇异积分方程的两种格式;最后给出数值实验验证理论分析结果. 相似文献
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通过对Ostrowski不等式的改进,扩大了Ostrowski积分公式的适用范围,将该积分公式应用于数值积分推广了经典的中点积分公式、梯形积分公式和Simpson积分公式,同时得到相应的最佳误差限,并给出了具体的数值应用. 相似文献
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1引 言积分的计算是自然科学中的一个基本问题.当积分的精确值不能求出时,数值积分就变得越来越重要了.数值积分的基本思想是直接利用被积函数(及其导数)在若干点处的函数值作线性组合得到积分的近似值.外推算法是一种可以提高数值计算精度的技巧,它利用几个精度较低的近似值作线性组合得到精度较高的近似值.定积分的复化求积公式及其外推算法可见[1]-[7],二重积分的复化求积公式可见[8,9,10],三重积分的复化求积公式可见[11,12]. 相似文献
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同学们从课本中熟悉了同底数幂相乘的运算法则,am·an=am+n(底数不变,指数相加).但要用好用活这个公式却不简单,本文特作一些介绍. 相似文献
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D. B. Hunter 《Numerical Algorithms》1995,10(1):41-49
A method of evaluating Legendre functions of the second kind by applying the trapezoidal rule to Heine's integral representation is described. An error analysis is given, and some numerical results are obtained.Dedicated to Professor Luigi Gatteschi 相似文献
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数值积分公式中间点的渐近性质及其应用 总被引:17,自引:1,他引:16
主要研究了三类数值积分公式的中间点的渐近性质,得到了更一般性的结果.基于中间点的渐近性质,获得了数值积分的校正公式及其条件误差估计.数值例子显示了校正公式的精度明显高于对应的计算公式. 相似文献
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We develop a fourth-order piecewise quartic spline rule for Hadamard
integral. The quadrature formula of Hadamard integral is obtained by replacing
the integrand function with the piecewise quartic spline interpolation function. We
establish corresponding error estimates and analyze the numerical stability. The
rule can achieve fourth-order convergence at any point in the interval, even when
the singular point coincides with the grid point. Since the derivative information of
the integrand is not required, the rule can be easily applied to solve many practical
problems. Finally, the quadrature formula is applied to solve the electromagnetic
scattering from cavities with different wave numbers, which improves the whole
accuracy of the solution. Numerical experiments are presented to show the efficiency
and accuracy of the theoretical analysis. 相似文献
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Mohammad Masjed-Jamei Zahra Moalemi Hari M. Srivastava Iván Area 《Mathematical Methods in the Applied Sciences》2020,43(3):1380-1398
In this paper, we first introduce a modification of linear multistep methods, which contain, in particular, the modified Adams-Bashforth methods for solving initial-value problems. The improved method is achieved by applying the Hermite quadrature rule instead of the Newton-Cotes quadrature formulas with equidistant nodes. The related coefficients of the method are then represented explicitly, the local error is given, and the order of the method is determined. If a numerical method is consistent and stable, then it is necessarily convergent. Moreover, a weighted type of the new method is introduced and proposed for solving a special case of the Cauchy problem for singular differential equations. Finally, several numerical examples and graphical representations are also given and compared. 相似文献
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Nassrallah-Rahman积分的一个新证明 总被引:2,自引:0,他引:2
应用关于q-微分算子的Leibniz公式证明了关于q-微分算子的两个恒等式.利用这些恒等式及q-级数的一些求和公式给出了Nasralah-Rahman积分的一个新证明,进而给出了关于q-级数8Φ7的积分表示的一个简易推导 相似文献
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E. Berriochoa Esnaola A. Cachafeiro López J.R. Illán-González E. Martínez-Brey 《Applied mathematics and computation》2011,218(8):4437-4447
In this paper we study convergence and computation of interpolatory quadrature formulas with respect to a wide variety of weight functions. The main goal is to evaluate accurately a definite integral, whose mass is highly concentrated near some points. The numerical implementation of this approach is based on the calculation of Chebyshev series and some integration formulas which are exact for polynomials. In terms of accuracy, the proposed method can be compared with rational Gauss quadrature formula. 相似文献
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We study the numerical solution of a linear hypersingular integral equation arising when solving the Neumann boundary value problem for the Laplace equation by the boundary integral equation method with the solution represented in the form of a double layer potential. The integral in this equation is understood in the sense of Hadamard finite value. We construct quadrature formulas for the integral occurring in this equation based on a triangulation of the surface and an application of the linear approximation to the unknown function on each of the triangles approximating the surface. We prove the uniform convergence of the quadrature formulas at the interpolation nodes as the triangulation size tends to zero. A numerical solution scheme for this integral equation based on the suggested quadrature formulas and the collocation method is constructed. Under additional assumptions about the shape of the surface, we prove a uniform estimate for the error in the numerical solution at the interpolation nodes. 相似文献
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In this study, we propose one of the new techniques used in solving numerical problems involving integral equations known as the Sinc-collocation method. This method has been shown to be a powerful numerical tool for finding fast and accurate solutions. So, in this article, a mixed Volterra-Fredholm integral equation which has been appeared in many science an engineering phenomena is discredited by using some properties of the Sinc-collocation method and Sinc quadrature rule to reduce integral equation to some algebraic equations. Then exponential convergence rate of this numerical technique is discussed by preparing a theorem. Finally, some numerical examples are included to demonstrate the validity and applicability of the convergence theorem and numerical scheme. 相似文献
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《Journal of Pure and Applied Algebra》2023,227(4):107256
We develop a duality for operations on nested pairs of modules that generalizes the duality between absolute interior operations and residual closure operations from [5], extending our previous results to the expanded context. We apply this duality in particular to integral and basically full closures and their respective cores to obtain integral and basically empty interiors and their respective hulls. We also dualize some of the known formulas for the core of an ideal to obtain formulas for the hull of a submodule of the injective hull of the residue field. The article concludes with illustrative examples in a numerical semigroup ring. 相似文献
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Summary Numerical integration formulas are discussed which are obtained by differentiation of the Volterra integral equation and by applying backward differentiation formulas to the resulting integro-differential equation. In particular, the stability of the method is investigated for a class of convolution kernels. The accuracy and stability behaviour of the method proposed in this paper is compared with that of (i) a block-implicit Runge-Kutta scheme, and (ii) the scheme obtained by applying directly a quadrature rule which is reducible to the backward differentiation formulas. The present method is particularly advantageous in the case of stiff Volterra integral equations. 相似文献