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211.
该文通过对非线性Schr■dinger方程增加耗散项,提出了一种新的三层线性差分格式.证明了该格式满足连续方程所具有的两个守恒量及收敛性和稳定性.通过数值例子与已知格式进行比较,结果表明该格式计算简单且具有较高精度. 相似文献
212.
利用在网格内恰当选取特征线上插值点的技巧,提出了一种新型的求解对流扩散方程的特征差分方法,并给出了稳定性与收敛性分析.该方法避免了数值扩散的产生,同时具有O(τ h~2)阶的收敛阶.数值实验表明,该方法是一个高效、稳定和收敛的数值方法. 相似文献
213.
Based on the calculation results of pair correlation energy contributions of the various electron pairs in Na2 and H2NNH2 systems and the application of the scaling ionic partition scheme for symmetrical A2 type systems, the total correlation energies of Na2 and H2NNH2 have been reproduced by using this simple scheme. The two results show that the absolute deviations are within an acceptable range of error, however, in this way, more than 90% of computational work can be saved. The most attractive result in present paper is that, in these two molecules the coefficients c1 and c2 in the estimation equation can be obtained by the proportion of correlation energy of A^- to that of A^ singlet system. Therefore, it is believed that the proposed ionic partition scheme for symmetrical A2 molecules would be very useful to estimate the correlation energies of large symmetrical molecules. 相似文献
214.
Wei Chen 《Numerical Methods for Partial Differential Equations》2005,21(3):512-520
Using the technique of eigenvalue error expansion and the technique of integral identities, we derive higher order convergence rate of the eigenvalue approximation for the biharmonic eigenvalue problem based on the Ciarlet‐Raviart discretization. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005 相似文献
215.
The aim of this paper is to model and simulate the displacement of radioactive elements in a saturated heterogeneous porous medium. New schemes are proposed to solve accurately the convection–diffusion–reaction equations including nonlinear terms in the time derivative. Numerical tests show the stability and robustness of these schemes through strong heterogeneities of the medium. Finally the COUPLEX 1 benchmark concerning the far field simulation of a polluted flow by a leak of a nuclear waste disposal is performed and compared with the results available in the literature. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
216.
This paper presents an error analysis for classification algorithms generated by regularization schemes with polynomial kernels.
Explicit convergence rates are provided for support vector machine (SVM) soft margin classifiers. The misclassification error
can be estimated by the sum of sample error and regularization error. The main difficulty for studying algorithms with polynomial
kernels is the regularization error which involves deeply the degrees of the kernel polynomials. Here we overcome this difficulty
by bounding the reproducing kernel Hilbert space norm of Durrmeyer operators, and estimating the rate of approximation by
Durrmeyer operators in a weighted L1 space (the weight is a probability distribution). Our study shows that the regularization parameter should decrease exponentially
fast with the sample size, which is a special feature of polynomial kernels.
Dedicated to Charlie Micchelli on the occasion of his 60th birthday
Mathematics subject classifications (2000) 68T05, 62J02.
Ding-Xuan Zhou: The first author is supported partially by the Research Grants Council of Hong Kong (Project No. CityU 103704). 相似文献
217.
Chein‐Shan Liu 《Numerical Methods for Partial Differential Equations》2007,23(5):1083-1109
We consider an inverse problem for estimating the two coefficient functions c and k in a parabolic type partial differential equation c(u)ut = ?[k(u)ux]/?x with the aid of the measurements of u at two different times. The first‐ and second‐order one‐step group preserving schemes are developed. Solving the resultant algebraic equations with a closed‐form, we can estimate the unknown temperature‐dependent thermal conductivity and heat capacity. The new methods possess threefold advantages: they do not require any a priori information on the functional forms of thermal conductivity and heat capacity; no initial guesses are required; and no iterations are required. Numerical examples are examined to show that the new approaches have high accuracy and efficiency, even there are rare measured data. When the measured temperatures are polluted by uniform or normal random noise, the estimated results are also good. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 相似文献
218.
Rui-ming YAO~ 《中国科学A辑(英文版)》2007,50(11):1661-1672
In this paper,we study a discontinuous Galerkin numerical scheme for a class of elliptic stochastic partial differential equations (abbr.elliptic SPDEs) driven by space white noises with ho- mogeneous Dirichlet boundary conditions for two and three space dimensions.We also establish L~2 error estimates for the scheme.In particular,a numerical test for d=2 is presented at the end of the article. 相似文献
219.
Guang-wei YUAN Xu-deng HANG Zhi-qiang SHENG Laboratory of Computational Physics Institute of Applied Physics Computational Mathematics Beijing China 《中国科学A辑(英文版)》2007,50(2):253-275
In this paper some new parallel difference schemes with interface extrapolation terms for a quasi-linear parabolic system of equations are constructed. Two types of time extrapolations are proposed to give the interface values on the interface of sub-domains or the values adjacent to the interface points, so that the unconditional stable parallel schemes with the second accuracy are formed. Without assuming heuristically that the original boundary value problem has the unique smooth vector solution, the existence and uniqueness of the discrete vector solutions of the parallel difference schemes constructed are proved. Moreover the unconditional stability of the parallel difference schemes is justified in the sense of the continuous dependence of the discrete vector solution of the schemes on the discrete known data of the original problems in the discrete W2(2,1) (Q△) norms. Finally the convergence of the discrete vector solutions of the parallel difference schemes with interface extrapolation terms to the unique generalized solution of the original quasi-linear parabolic problem is proved. Numerical results are presented to show the good performance of the parallel schemes, including the unconditional stability, the second accuracy and the high parallelism. 相似文献
220.
本文应用Laksov和Fulton发展的方法,对态射f:C→S得到了Fulton(1)中二重点公式的一个推广,此处C,S分别是光滑的曲线和曲面。在文章的后一部分对得到的公式作了一些评注。 相似文献