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61.
《Journal of Computational and Applied Mathematics》2005,174(2):383-397
This paper is devoted to the testing and comparison of numerical solutions obtained from higher-order accurate finite difference schemes for the two-dimensional Burgers' equation having moderate to severe internal gradients. The fourth-order accurate two-point compact scheme, and the fourth-order accurate Du Fort Frankel scheme are derived. The numerical stability and convergence are presented. The cases of shock waves of severe gradient are solved and checked with the fourth-order accurate Du Fort Frankel scheme solutions. The present study shows that the fourth-order two-point compact scheme is highly stable and efficient in comparison with the fourth-order accurate Du Fort Frankel scheme. 相似文献
62.
Marianne Gerny Burkhard Alpers 《International Journal of Computers for Mathematical Learning》2004,9(1):25-57
In this article we describe a mathematical microworld for investigating car motion on a racing course and its use with a group of grade 12 students. The microworld is concerned with the mathematical construction of courses and functions which describe car motion. It is implemented in the computer algebra system, Maple®, which provides the means to represent courses and functions symbolically and graphically. We describe the learning opportunities offered by the microworld in relation to the research literature on functions. Various facets and layers of the function concept are addressed in the microworld, and we suggest how work in the microworld might help in overcoming some well-known misconceptions.This revised version was published online in September 2005 with corrections to the Cover Date. 相似文献
63.
稀磁半导体Zn1-xMnxTe吸收光谱压力红移的理论研究 总被引:1,自引:1,他引:0
以自由Mn2+离子的径向波函数为基础,通过引入电子云延伸效应系数κ来修正这一径向波函数,得到了稀磁半导体Zn1-xMnxTe晶体中Mn2+离子的径向波函数.以此波函数为基础,研究了Zn1-xMnxTe晶体吸收光谱的高压谱移特性,并且得到了吸收谱中四条谱线随压力的红移规律. 相似文献
64.
进一步研究了具有三个cM公共值的亚纯函数的唯一性,改进了H.Ueda和仪洪勋等人的有关结果. 相似文献
65.
基于增广Lagrange函数的RQP方法 总被引:3,自引:0,他引:3
Recursive quadratic programming is a family of techniques developd by Bartholomew-Biggs and other authors for solving nonlinear programming problems.This paperdescribes a new method for constrained optimization which obtains its search di-rections from a quadratic programming subproblem based on the well-known aug-mented Lagrangian function.It avoids the penalty parameter to tend to infinity.We employ the Fletcher‘s exact penalty function as a merit function and the use of an approximate directional derivative of the function that avoids the need toevaluate the second order derivatives of the problem functions.We prove that thealgorithm possesses global and superlinear convergence properties.At the sametime, numerical results are reported. 相似文献
66.
Regularity of Harmonic Functions in Cheeger-Type Sobolev Spaces 总被引:3,自引:0,他引:3
We give a geometric approach to the study of the regularity of harmonic functions in Cheeger-type Sobolev spaces, and prove the Hölder continuity of such functions. In the proof, we give a definition of an upper curvature bound of the unit sphere of a Banach space, which seems to be of independent interest. 相似文献
67.
In this note we show that many classes of global optimization problems can be treated most satisfactorily by classical optimization theory and conventional algorithms. We focus on the class of problems involving the minimization of the product of several convex functions on a convex set which was studied recently by Kunoet al. [3]. It is shown that these problems are typical composite concave programming problems and thus can be handled elegantly by c-programming [4]–[8] and its techniques. 相似文献
68.
汪巍 《数学的实践与认识》2004,34(3):103-109
首先引入了差分系统基于两种度量的极端稳定性概念 ,然后建立了一些关于差分系统 ( h0 ,h)极端稳定性 (极端一致稳定性 ,极端渐近稳定性 ,极端一致渐近稳定性 )的判定准则 .在所得到的定理中 ,对△ V的限制较弱 ,特别地 ,△V甚至可以恒为正 ,从而便于实际应用 . 相似文献
69.
Let P(z) be a polynomial of degree n with complex coefficients and consider the n–th order linear differential operator P(D). We show that the equation P(D)f = 0 has the Hyers–Ulam stability, if and only if the equation P(z) = 0 has no pure imaginary solution. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
70.
In the present work we consider the problem of interpolating scattered data using radial basis functions (RBF). In general, it is well known that this leads to a discrete linear inverse problem that needs to be regularized in order to provide a meaningful solution. The work focuses on a metric-regularization approach, based on a new class of RBF, called anisotropic RBF. The work provides theoretical justifications for the regularization approach and it considers a suitable proposal for the metric, supporting it by numerical examples. 相似文献