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从一道考研试题入手,给出了当二重积分的被积函数或积分区域边界含x2-y2时的"双曲坐标变换"法.通过实例,对比说明该方法能够解决一类用直角坐标不易计算或不能计算的二重积分问题,并且可以运用到三重积分的计算上. 相似文献
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针对授课班级出错率较高的一道曲面积分题目,给出四种解法.分析出错的原因在于练习不够外,主要是对重积分概念理解不够透彻. 相似文献
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通过实例介绍如何用二重积分计算某些特殊的定积分.为定积分的计算提供一种思路,展示了二重积分与定积分在一定程度上的内在联系. 相似文献
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Zeng Yong Xie Yunsun 《大学数学》1998,(2)
本文将二重积分、三重积分、第一类曲线积分及第一类曲面积分统一为多元数量值函数的积分,并且用第一类曲线、曲面积分定义第二类曲线、曲面积分。 相似文献
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D. Rostami Varnos Fadrani K. Maleknejad 《Journal of Computational Analysis and Applications》1999,1(2):219-234
A very efficient and fully discrete method for numerical solution of boundary nonlinear integral equation is described. There seems a lack of rigorous numerical analysis because of singular or hypersingular behavior. In this paper, we suggest variants of methods for solving numerical solutions. Moreover, our aim has been to show how the iterations can be effectively and efficiently regularized for solving ill-posed problems by using the preconditioner. We have compared these methods with CPU time and iterations. Finally, some numerical examples show the efficiency of the proposed methods. 相似文献
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再生核空间中一类非线性积分方程的求解方法 总被引:1,自引:0,他引:1
本文在再生核空间中,利用再生核把非线性积分方程化为线性积分方程,研究了此类方程的求解问题,揭示了此类方程解的结构,存在性及多解等问题. 相似文献
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约定f为连续函数,分别利用交换积分次序、变量替换、等位线法等三种方法证明二重积分计算公式∫0^a∫0^a f(x+y)dxdy=∫0^a(a-t)f(t+a)dt+∫0^atf(t)dt,并得到一个类似公式∫0^a∫0^af(x-y)dxdy=∫0^atf(t-a)dt+∫0^a(a-t)f(t)dt. 相似文献
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用积分方程法解板的振动问题* 总被引:5,自引:0,他引:5
本文把带有集中质量、弹性支承和弹簧支撑着的质量块(振子)的薄板的振动微分方程化成为积分方程的特征值问题。然后利用广义函数理论和积分方程理论,得到了用一无穷阶矩阵的标准特征值形式给出的频率方程,从而方便地得到了固有频率和振型。并讨论了这种方法的收敛性。 相似文献
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AbstractSeveral discontinuous Galerkin (DG) methods are introduced for solving a frictional contact problem with normal compliance, which is modeled as a quasi-variational inequality. Consistency, boundedness, and stability are established for the DG methods. Two numerical examples are presented to illustrate the performance of the DG methods. 相似文献
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This paper concerns a class of deferred correction methods recently developed for initial value ordinary differential equations;
such methods are based on a Picard integral form of the correction equation. These methods divide a given timestep [tn,tn+1] into substeps, and use function values computed at these substeps to approximate the Picard integral by means of a numerical
quadrature. The main purpose of this paper is to present a detailed analysis of the implications of the location of quadrature
nodes on the accuracy and stability of the overall method. Comparisons between Gauss-Legendre, Gauss-Lobatto, Gauss-Radau,
and uniformly spaced points are presented. Also, for a given set of quadrature nodes, quadrature rules may be formulated that
include or exclude function values computed at the left-hand endpoint tn. Quadrature rules that do not depend on the left-hand endpoint (which are referred to as right-hand quadrature rules) are
shown to lead to L(α)-stable implicit methods with α≈π/2. The semi-implicit analog of this property is also discussed. Numerical results suggest
that the use of uniform quadrature nodes, as opposed to nodes based on Gaussian quadratures, does not significantly affect
the stability or accuracy of these methods for orders less than ten. In contrast, a study of the reduction of order for stiff
equations shows that when uniform quadrature nodes are used in conjunction with a right-hand quadrature rule, the form and
extent of order-reduction changes considerably. Specifically, a reduction of order to
is observed for uniform nodes as opposed to
for non-uniform nodes, where Δt denotes the time step and ε a stiffness parameter such that ε→0 corresponds to the problem becoming increasingly stiff.
AMS subject classification (2000) 65B05 相似文献
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投资的收益和风险的数学模型及算法研究 总被引:2,自引:0,他引:2
本文按照“满意解”、“多组解”的思路对投资的收益和风险问题进行了分析和处理 ,提出了将净收益与总体风险划分为若干等级 ,并按等级求出多组满意解的思想方法 ,最后对模型的数学性质与计算方法进行了初步研究 相似文献