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本文借助于Hadamard关于高阶奇异积分有限部分的思想,研究关于实 Clifford分析中六个类型(含一个奇点或二个奇点的)拟Bochner-Martinelli型高阶奇异积分的归纳定义、Hadamard主值的存在性、递推公式、计算公式、微分公式、Poincare-Bertrand置换公式以及拟B-M型高阶奇异积分的Holder连续性等问题.这些问题是研究单、多元复分析的学者们在研究奇异积分时,通常要涉及到的几个问题.  相似文献
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本提出一种新的消元方法,该法利用数值的直接迭代产生余量方程,从而构成已消去很多未知量的线性方程组。本的方法具有求解简便、精确和快速的优点。  相似文献
3.
In this paper the stability of the 3-step backward differentiation formula (BDF) on variable grids for the numerical integration of time-dependent parabolic problems is analysed. A stability inequality with a stability constant depending in a controllable way on the mesh is obtained. In particular if the ratios r j of adjacent mesh-sizes of the underlying grid satisfy the bound r j < 1.199 then any mixture of the j-step BDF for j {1, 2, 3} is stable provided the number of changes between increasing and decreasing mesh-sizes is uniformly bounded. From the stability inequality error estimates can be obtained.  相似文献
4.
孙立群  孔志宏 《大学数学》2007,23(1):161-165
主要指出了微分法与参数法的实质及二者的本质区别,以及求奇解的一个注意事项.  相似文献
5.
New modified open Newton Cotes integrators are introduced in this paper. For the new proposed integrators the connection between these new algorithms, differential methods and symplectic integrators is studied. Much research has been done on one step symplectic integrators and several of them have obtained based on symplectic geometry. However, the research on multistep symplectic integrators is very poor. Zhu et al. [1] studied the well known open Newton Cotes differential methods and they presented them as multilayer symplectic integrators. Chiou and Wu [2] studied the development of multistep symplectic integrators based on the open Newton Cotes integration methods. In this paper we introduce a new open modified numerical method of Newton Cotes type and we present it as symplectic multilayer structure. The new obtained symplectic schemes are applied for the solution of Hamilton’s equations of motion which are linear in position and momentum. An important remark is that the Hamiltonian energy of the system remains almost constant as integration proceeds. We have applied also efficiently the new proposed method to a nonlinear orbital problem and an almost periodic orbital problem.  相似文献
6.
通过对不定积分的研究,提出了求几类特殊函数不定积分的新方法.不但求出了高等数学中具有代表性的几种形式的不定积分,而且对不定积分的教学和积分方法的寻求都有启发作用.  相似文献
7.
The connection between closed Newton–Cotes, trigonometrically-fitted differential methods and symplectic integrators is studied in this paper. Several one-step symplectic integrators have been obtained based on symplectic geometry, as is shown in the literature. However, the study of multi-step symplectic integrators is very limited. The well-known open Newton–Cotes differential methods are presented as multilayer symplectic integrators by Zhu et al. [W. Zhu, X. Zhao, Y. Tang, Journal of Chem. Phys. 104 (1996), 2275]. The construction of multi-step symplectic integrators based on the open Newton–Cotes integration methods is investigated by Chiou and Wu [J.C. Chiou, S.D. Wu, Journal of Chemical Physics 107 (1997), 6894]. The closed Newton–Cotes formulae are studied in this paper and presented as symplectic multilayer structures. We also develop trigonometrically-fitted symplectic methods which are based on the closed Newton–Cotes formulae. We apply the symplectic schemes in order to solve Hamilton’s equations of motion which are linear in position and momentum. We observe that the Hamiltonian energy of the system remains almost constant as the integration proceeds. Finally we apply the new developed methods to an orbital problem in order to show the efficiency of this new methodology.  相似文献
8.
“升阶法”能够把一类特殊的一阶线性微分方程化为二阶常系数齐次线性微分方程求解,而一般的一阶线性微分方程的求解问题可以转化为二元函数全微分的求积问题。利用“升阶法”和“全微分法”对学生进行逆向思维训练,培养学生的创新思维能力。  相似文献
9.
In this work successive differentiation method is applied to solve highly nonlinear partial differential equations (PDEs) such as Benjamin–Bona–Mahony equation, Burger's equation, Fornberg–Whitham equation, and Gardner equation. To show the efficacy of this new technique, figures have been incorporated to compare exact solution and results of this method. Wave variable is used to convert the highly nonlinear PDE into ordinary differential equation with order reduction. Then successive differentiation method is utilized to obtain the numerical solution of considered PDEs in this paper. Copyright © 2017 John Wiley & Sons, Ltd.  相似文献
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