数值流形方法的变分原理与应用

针对线弹性体静力问题,根据数值流形方法的特点及相应的位移模式,得到了面向物理覆盖的数值流形方法的变分原理,详细推导了基于变分原理的数值流形方法的理论计算公式,建立了数值流形方法的控制方程。作为实际应用,给出了相应的数值算例,结果表明,求解精度和效益令人满意。     

三维数值流形方法的理论研究

在二维数值流形方法的基础上,对三维数值流形进行了理论研究．研究了三维覆盖位移函数,进行了三维数值流形的力学分析,给出了三维流形单元的刚度矩阵,详细推导了三维数值流形的Hammer积分及剖分规则,系统地研究三维数值流形的理论体系与数值实现方法．作为数值算例,给出了相应的悬臂梁的计算结果,计算结果表明算法的精度和计算效益较高．     

复频域卷积的离散算法

导出了适用于计算机进行计算的复频域卷积的离散算法,应用Durbin拉氏变换数值反演法对复频域卷积结果进行数值反演,可获得时域数值解.将该数值解与解析解进行比较表明,数值解具有较高的精度.     

渗流问题灰色数值模型的解法研究

灰色数值模型的求解是研究灰色数值模型的一个重要问题 .本文根据灰集合、灰数及其灰色运算规则 ,在渗流系统的基本灰色数值模型的基础上 ,分析了求解这类模型的一整套灰色数值算法 ,并对灰色数值算法、普通算法和经典数值方法的计算结果进行了全面比较 ,论证了灰色数值算法对灰信息传递的正确性和对渗流系统描述的合理性 .     

露天矿卡车运输系统最佳调度的教学模型及其数值解法研究

章分析了目前卡车调度系统的建模情况,应用最佳控制的理论建立了卡车调度系统的数学模型,并结合一简例,分析了数值解法,给出简例的数值解。通过对数值解的分析,说明数学模型和数值解法都是正确的。     

三阶Airy方程满足两个守恒律的非线性差分格式

近年来,学者们对发展型偏微分方程设计了一种能保持多个守恒律的数值方法,这类方法无论在解的精度还是长时间的数值模拟方面都表现出非常好的性质.将这类思想应用到三阶Airy方程,即三阶散射方程,对其设计了满足两个守恒律的非线性差分格式.该格式不仅计算数值解,同时计算数值能量,并且保证数值解和数值能量同时守恒.从数值结果可以看出,该格式在长时间的数值模拟中具有更好的保结构性质.     

非线性数值流形方法的变分原理与应用

针对非线性力学问题,根据数值流形方法的特点及相应的位移模式,得到了面向物理覆盖的非线性数值流形方法的变分原理,详细推导了基于变分原理的非线性数值流形方法的理论计算公式,建立了非线性数值流形方法的理论体系和控制方程。作为实际应用,给出了相应的数值算例,结果表明,求解精度和效益令人满意。     

露天矿卡车运输系统最佳调度的数学模型及其数值解法研究

文章分析了目前卡车调度系统的建模情况,应用最佳控制的理论建立了卡车调度系统的数学模型,并结合一简例,分析了数值解法,给出简例的数值解。通过对数值解的分析,说明数学模型和数值解法都是正确的     

Laplace变换的数值反演

本文根据作者使用 Laplace 变换数值反演的实际经验,对若干数值反演方法进行评论.实践经验表明,基于 Jacobi 正交多项式的数值反演方法计算精度较好,但仍然存在问题。 作者在实际工作中作了某些改进.对某些新近发表的数值反演方法,本文也作了简短评述,有关它们的数值试验,正在进行之中.     

《高等数值分析》教学案例的建设与思考

《高等数值分析》是一门与实际联系紧密的数学公共课程,它理论深刻,应用广泛.本文结合实际应用,为《高等数值分析》中常微分方程数值解部分设计了一个教学案例,通过理论分析和数值实验向学生展示了刚性问题的概念和相关数值方法,并对《高等数值分析》课程教学案例的设计进行了思考.     

Short Book Reviews

Problems in Linear Algebra, by I. V. Proskuryakov. Mir Publishers, Moscow, 1978= 453 pp.

Inequalities: Theory of Majorization and its Applications. by A. W. Marshall and I. Olkin. Academic Press, 1979, 569 pp.

Problems in Linear Algebra, by I. V. Proskuryakov. Mir Publishers, Moscow, 1978. 453 pp. Inequalities: Theory of Majorization and its Applications. by A. W. Marshall and I. Olkin. Academic Press, 1979, 569 pp. Introduction to Numerical Analysis. by F. Stummel and K. Hainer. Scottish Academic Press (in United States, Columbia University Press), 1980. 282 pp., soft cover.

Introduction to Numerical Analysis. by F. Stummel and K. Hainer. Scottish Academic Press (in the United States, Columbia University Press), 1980. 282 pp., soft cover.     

Binary formally self-dual odd codes

Most of the research on formally self-dual (f.s.d.) codes has been developed for binary f.s.d. even codes, but only limited research has been done for binary f.s.d. odd codes. In this article we complete the classification of binary f.s.d. odd codes of lengths up to 14. We also classify optimal binary f.s.d. odd codes of length 18 and 24, so our result completes the classification of binary optimal f.s.d. odd codes of lengths up to 26. For this classification we first find a relation between binary f.s.d. odd codes and binary f.s.d. even codes, and then we use this relation and the known classification results on binary f.s.d. even codes. We also classify (possibly) optimal binary double circulant f.s.d. odd codes of lengths up to 40.     

Free boundary problems in the theory of fluid flow through porous media: Existence and uniqueness theorems

Summary Elliptic free boundary problems in the theory of fluid flow through porous media are studied by a new method, which reduces the problems to variational inequalities: existence and uniqueness theorems are proved. Entrata in Redazione il 3 agosto 1972. Research supported by C.N.R. in the frame of the collaboration between L.A.N. of Pavia and E.R.A. 215 of C.N.R.S. and of Paris University. ? Laboratorio di Analisi Numerica del C.N.R. di Pavia ? and ? Università di Pavia ?. ? Università di Pavia ? and ? G.N.A.F.A. del C.N.R. ?.     

Viscosity approximation methods for a finite family of nonexpansive mappings in Banach spaces

By using viscosity approximation methods for a finite family of nonexpansive mappings in Banach spaces, some sufficient and necessary conditions for the iterative sequence to converging to a common fixed point are obtained. The results presented in the paper extend and improve some recent results in [H.K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl. 298 (2004) 279-291; H.K. Xu, Remark on an iterative method for nonexpansive mappings, Comm. Appl. Nonlinear Anal. 10 (2003) 67-75; H.H. Bauschke, The approximation of fixed points of compositions of nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 202 (1996) 150-159; B. Halpern, Fixed points of nonexpansive maps, Bull. Amer. Math. Soc. 73 (1967) 957-961; J.S. Jung, Iterative approaches to common fixed points of nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 302 (2005) 509-520; P.L. Lions, Approximation de points fixes de contractions', C. R. Acad. Sci. Paris Sér. A 284 (1977) 1357-1359; A. Moudafi, Viscosity approximation methods for fixed point problems, J. Math. Anal. Appl. 241 (2000) 46-55; S. Reich, Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl. 75 (1980) 128-292; R. Wittmann, Approximation of fixed points of nonexpansive mappings, Arch. Math. 58 (1992) 486-491].     

The multidimensional plateau problem in Riemannian varieties

This paper is the author's abstract of his dissertation for the degree of Doctor of Physico-Mathematical Sciences. The dissertation was defended on September 29, 1972 at a session of the Council of the Mechanico-Mathematical Faculty of M. V. Lomonosov Moscow University. The official opponents were Prof. V. M. Alekseev, Doctor of Phys.-Mat. Sci.; Prof. D. V. Anosov, Doctor of Phys.-Mat. Sci.; and Prof. M. M. Postnikov, Doctor of Phys.-Mat. Sci.Translated from Matematicheskie Zametki, Vol. 13, No. 1, pp. 159–167, January, 1973.     

Sensitivity analysis for parametric generalized implicit quasi-variational-like inclusions involving P-η-accretive mappings

In this paper, using proximal-point mapping technique of P-η-accretive mapping and the property of the fixed-point set of set-valued contractive mappings, we study the behavior and sensitivity analysis of the solution set of a parametric generalized implicit quasi-variational-like inclusion involving P-η-accretive mapping in real uniformly smooth Banach space. Further, under suitable conditions, we discuss the Lipschitz continuity of the solution set with respect to the parameter. The technique and results presented in this paper can be viewed as extension of the techniques and corresponding results given in [R.P. Agarwal, Y.-J. Cho, N.-J. Huang, Sensitivity analysis for strongly nonlinear quasi-variational inclusions, Appl. Math. Lett. 13 (2002) 19-24; S. Dafermos, Sensitivity analysis in variational inequalities, Math. Oper. Res. 13 (1988) 421-434; X.-P. Ding, Sensitivity analysis for generalized nonlinear implicit quasi-variational inclusions, Appl. Math. Lett. 17 (2) (2004) 225-235; X.-P. Ding, Parametric completely generalized mixed implicit quasi-variational inclusions involving h-maximal monotone mappings, J. Comput. Appl. Math. 182 (2) (2005) 252-269; X.-P. Ding, C.L. Luo, On parametric generalized quasi-variational inequalities, J. Optim. Theory Appl. 100 (1999) 195-205; Z. Liu, L. Debnath, S.M. Kang, J.S. Ume, Sensitivity analysis for parametric completely generalized nonlinear implicit quasi-variational inclusions, J. Math. Anal. Appl. 277 (1) (2003) 142-154; R.N. Mukherjee, H.L. Verma, Sensitivity analysis of generalized variational inequalities, J. Math. Anal. Appl. 167 (1992) 299-304; M.A. Noor, Sensitivity analysis framework for general quasi-variational inclusions, Comput. Math. Appl. 44 (2002) 1175-1181; M.A. Noor, Sensitivity analysis for quasivariational inclusions, J. Math. Anal. Appl. 236 (1999) 290-299; J.Y. Park, J.U. Jeong, Parametric generalized mixed variational inequalities, Appl. Math. Lett. 17 (2004) 43-48].     

On the convergence of implicit iteration process with error for a finite family of asymptotically nonexpansive mappings

The purpose of this paper is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of [H. Bauschke, The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space, J. Math. Anal. Appl. 202 (1996) 150-159; B. Halpern, Fixed points of nonexpansive maps, Bull. Amer. Math. Soc. 73 (1967) 957-961; P.L. Lions, Approximation de points fixes de contractions, C. R. Acad. Sci. Paris, Ser. A 284 (1977), 1357-1359; S. Reich, Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl. 75 (1980) 287-292; Z.H. Sun, Strong convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings, J. Math. Anal. Appl. 286 (2003) 351-358; R. Wittmann, Approximation of fixed points of nonexpansive mappings, Arch. Math. 58 (1992) 486-491; H.K. Xu, M.G. Ori, An implicit iterative process for nonexpansive mappings, Numer. Funct. Anal. Optimiz. 22 (2001) 767-773; Y.Y. Zhou, S.S. Chang, Convergence of implicit iterative process for a finite family of asymptotically nonexpansive mappings in Banach spaces, Numer. Funct. Anal. Optimiz. 23 (2002) 911-921].     

Recent advances in linear analysis of convergence for splittings for solving ODE problems

In the nineties, Van der Houwen et al. (see, e.g., [P.J. van der Houwen, B.P. Sommeijer, J.J. de Swart, Parallel predictor–corrector methods, J. Comput. Appl. Math. 66 (1996) 53–71; P.J. van der Houwen, J.J.B. de Swart, Triangularly implicit iteration methods for ODE-IVP solvers, SIAM J. Sci. Comput. 18 (1997) 41–55; P.J. van der Houwen, J.J.B. de Swart, Parallel linear system solvers for Runge–Kutta methods, Adv. Comput. Math. 7 (1–2) (1997) 157–181]) introduced a linear analysis of convergence for studying the properties of the iterative solution of the discrete problems generated by implicit methods for ODEs. This linear convergence analysis is here recalled and completed, in order to provide a useful quantitative tool for the analysis of splittings for solving such discrete problems. Indeed, this tool, in its complete form, has been actively used when developing the computational codes BiM and BiMD [L. Brugnano, C. Magherini, The BiM code for the numerical solution of ODEs, J. Comput. Appl. Math. 164–165 (2004) 145–158. Code available at: http://www.math.unifi.it/~brugnano/BiM/index.html; L. Brugnano, C. Magherini, F. Mugnai, Blended implicit methods for the numerical solution of DAE problems, J. Comput. Appl. Math. 189 (2006) 34–50]. Moreover, the framework is extended for the case of special second order problems. Examples of application, aimed to compare different iterative procedures, are also presented.     

IFS on a metric space with a graph structure and extensions of the Kelisky-Rivlin theorem

We develop the Hutchinson-Barnsley theory for finite families of mappings on a metric space endowed with a directed graph. In particular, our results subsume a classical theorem of J.E. Hutchinson [J.E. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J. 30 (1981) 713-747] on the existence of an invariant set for an iterated function system of Banach contractions, and a theorem of L. Máté [L. Máté, The Hutchinson-Barnsley theory for certain non-contraction mappings, Period. Math. Hungar. 27 (1993) 21-33] concerning finite families of locally uniformly contractions introduced by Edelstein. Also, they generalize recent fixed point theorems of A.C.M. Ran and M.C.B. Reurings [A.C.M. Ran, M.C.B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435-1443], J.J. Nieto and R. Rodríguez-López [J.J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223-239; J.J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.) 23 (2007) 2205-2212], and A. Petru?el and I.A. Rus [A. Petru?el, I.A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. 134 (2006) 411-418] for contractive mappings on an ordered metric space. As an application, we obtain a theorem on the convergence of infinite products of linear operators on an arbitrary Banach space. This result yields new generalizations of the Kelisky-Rivlin theorem on iterates of the Bernstein operators on the space C[0,1] as well as its extensions given recently by H. Oruç and N. Tuncer [H. Oruç, N. Tuncer, On the convergence and iterates of q-Bernstein polynomials, J. Approx. Theory 117 (2002) 301-313], and H. Gonska and P. Pi?ul [H. Gonska, P. Pi?ul, Remarks on an article of J.P. King, Comment. Math. Univ. Carolin. 46 (2005) 645-652].     

Stability of iterative procedures with errors for approximating common fixed points of a couple of q-contractive-like mappings in Banach spaces

Recently, Agarwal, Cho, Li and Huang [R.P. Agarwal, Y.J. Cho, J. Li, N.J. Huang, Stability of iterative procedures with errors approximating common fixed points for a couple of quasi-contractive mappings in q-uniformly smooth Banach spaces, J. Math. Anal. Appl. 272 (2002) 435-447] introduced the new iterative procedures with errors for approximating the common fixed point of a couple of quasi-contractive mappings and showed the stability of these iterative procedures with errors in Banach spaces. In this paper, we introduce a new concept of a couple of q-contractive-like mappings (q>1) in a Banach space and apply these iterative procedures with errors for approximating the common fixed point of the couple of q-contractive-like mappings. The results established in this paper improve, extend and unify the corresponding ones of Agarwal, Cho, Li and Huang [R.P. Agarwal, Y.J. Cho, J. Li, N.J. Huang, Stability of iterative procedures with errors approximating common fixed points for a couple of quasi-contractive mappings in q-uniformly smooth Banach spaces, J. Math. Anal. Appl. 272 (2002) 435-447], Chidume [C.E. Chidume, Approximation of fixed points of quasi-contractive mappings in Lp spaces, Indian J. Pure Appl. Math. 22 (1991) 273-386], Chidume and Osilike [C.E. Chidume, M.O. Osilike, Fixed points iterations for quasi-contractive maps in uniformly smooth Banach spaces, Bull. Korean Math. Soc. 30 (1993) 201-212], Liu [Q.H. Liu, On Naimpally and Singh's open questions, J. Math. Anal. Appl. 124 (1987) 157-164; Q.H. Liu, A convergence theorem of the sequence of Ishikawa iterates for quasi-contractive mappings, J. Math. Anal. Appl. 146 (1990) 301-305], Osilike [M.O. Osilike, A stable iteration procedure for quasi-contractive maps, Indian J. Pure Appl. Math. 27 (1996) 25-34; M.O. Osilike, Stability of the Ishikawa iteration method for quasi-contractive maps, Indian J. Pure Appl. Math. 28 (1997) 1251-1265] and many others in the literature.