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191.
192.
综述了排队系统中的泰勒展开方法。它由Gong和Hu在1990s首次提出,并在最近几年里有了一些新的发展。首先,通过GI/GI/1队列的简单例子介绍其基本原理;其次,展示如何应用该方法分析相关性队列和离去过程;然后,阐述如何基于该方法发展排队网络近似的高阶矩方法;最后,讨论未来的几个可能研究方向。 相似文献
193.
194.
某文献在处理一道关于高阶导数的应用问题时,反复利用Rolle定理来证明高阶导数为零.考虑到这种做法过于繁琐,遂通过对其证明方法的改进,综合使用Lagrange中值定理和Taylor公式,使该问题的解决获得简化. 相似文献
195.
针对某教材中关于凹函数不等式的一道证明题,分别采用单调性、泰勒公式和中值定理给出三种证明方法,旨在帮助学生拓展其思维广度,培养其综合能力,提高其数学素质. 相似文献
196.
The six Painlevé transcendents PI − PVI have both applications and analytic properties that make them stand out from most other classes of special functions. Although they have been the subject of extensive theoretical investigations for about a century, they still have a reputation for being numerically challenging. In particular, their extensive pole fields in the complex plane have often been perceived as ‘numerical mine fields’. In the present work, we note that the Painlevé property in fact provides the opportunity for very fast and accurate numerical solutions throughout such fields. When combining a Taylor/Padé-based ODE initial value solver for the pole fields with a boundary value solver for smooth regions, numerical solutions become available across the full complex plane. We focus here on the numerical methodology, and illustrate it for the PI equation. In later studies, we will concentrate on mathematical aspects of both the PI and the higher Painlevé transcendents. 相似文献
197.
Elham Keshavarz Yadollah Ordokhani 《Mathematical Methods in the Applied Sciences》2019,42(13):4427-4443
In this paper, a fast numerical algorithm based on the Taylor wavelets is proposed for finding the numerical solutions of the fractional integro‐differential equations with weakly singular kernels. The properties of Taylor wavelets are given, and the operational matrix of fractional integration is constructed. These wavelets are utilized to reduce the solution of the given fractional integro‐differential equation to the solution of a linear system of algebraic equations. Also, convergence of the proposed method is studied. Illustrative examples are included to demonstrate the validity and applicability of the technique. 相似文献
198.
Jie Yang Heng Hu Michel Potier‐Ferry 《Numerical Methods for Partial Differential Equations》2019,35(1):84-113
A recently proposed meshless method is discussed in this article. It relies on Taylor series, the shape functions being high degree polynomials deduced from the Partial Differential Equation (PDE). In this framework, an efficient technique to couple several polynomial approximations has been presented in (Tampango, Potier‐Ferry, Koutsawa, Tiem, Int. J. Numer. Meth. Eng. vol. 95 (2013) pp. 1094–1112): the boundary conditions were applied using the least‐square collocation and the interface was coupled by a bridging technique based on Lagrange multipliers. In this article, least‐square collocation and Lagrange multipliers are applied for boundary conditions, respectively, and least‐square collocation is revisited to account for the interface conditions in piecewise resolutions. Various combinations of these two techniques have been investigated and the numerical results prove their effectiveness to obtain very accurate solutions, even for large scale problems. 相似文献
199.
The diffusion coefficients of aqueous ammonium and potassium ions at infinite dilution differ by only 0.01% at 25°C, so, according
to Nernst's law, the binary mutual diffusion coefficients D of pairs of dilute aqueous ammonium and potassium salts should
be nearly identical. Yet precise optical interferometric data for ammonium and potassium sulfates contradict this rule: the
value of D reported previously for 0.05 mol-L−1 aqueous ammonium sulfate is 0.80×10−5 cm2-s−1, while the corresponding value for potassium sulfate is 1.24×10−5 cm2-s−1 about 50% higher. To confirm this surprising result, the diffusion coefficients of the two salts have been measured by the
Taylor dispersion technique. The diffusion coefficients of the salts are indeed nearly identical, and the earlier ammonium
sulfate data are found to be incorrect. 相似文献
200.
P. N. Paraskevopoulos A. S. Tsirikos K. G. Arvanitis 《Journal of Optimization Theory and Applications》1991,71(2):315-340
A new Taylor series approach is presented which reduces the problem of determining the state vector coefficient matrixX for time-invariant systems to an expression involving multiplications of matrices of small dimensions. This approach is numerically superior to known techniques and is extended to cover the time-varying case, wherein analogous expressions are derived. Furthermore, the optimal control problem is solved using the same technique. Finally, an expression is derived for the computation of the approximation error involved in computingX, prior to determiningX.This work was partially supported by the Greek State Scholarship Foundation (IKY). 相似文献