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2006年工作年报



一、机构设置和聘任工作
二、科学研究方向、科研项目和经费
三、科学研究成果
四、学术活动
五、学科建设和人才培养
六、工作环境及实验室建设
七、2006年论文摘要

一、机构设置和聘任工作
1.根据《上海高校计算科学E—研究院建设总体规划书》和《上海高校计算科学E
—研究院管理章程》等文件,制订和执行2006年度工作计划。
2.郭本瑜教授为首席研究员,并聘请下列专家为特聘研究员:
  • 张伟江 上海交通大学教授
  • 程  晋 复旦大学教授
  • 黄建国 上海交通大学教授
  • 丛玉豪 上海师范大学教授
  • 岳荣先 上海师范大学教授
  • 王元明 华东师范大学教授
  • 徐承龙 同济大学教授
  • 田红炯 上海师范大学教授
  • 王中庆 上海师范大学副教授
3.由下列专家组成学术委员会:
  • 主任:石钟慈中国科学院院士
  • 委员:林  群中国科学院院士
  • 姜礼尚 同济大学教授
  • 郭本瑜 上海师范大学教授
  • 张伟江 上海交通大学教授
  • 吴宗敏 复旦大学教授
  • 马和平 上海大学教授
  • 香港城市大学王世全教授为研究院顾问。
4.田红炯教授兼任业务秘书,王维敏同志任行政秘书。
二、科学研究方向、科研项目和经费
1.根据E—研究院科学研究方向,制订并资助本年度研究课题,承担国家和上海市其它科研项目,积极申请新的科研项目。
2.目前的主要研究方向:
  • 数学物理问题的高精度算法
  • 动力系统的数值研究
  • 弹性组合结构的数值方法
  • 金融随机模型的数值方法
  • 伪蒙特卡罗方法
  • 反问题的数值方法
3.本年度资助下列研究课题,共30.5万。
  • 郭本瑜 数学物理问题的高精度算法4万
  • 程  晋 数学物理反问题的理论和数值方法4万
  • 黄建国 组合弹性结构问题的有限元方法3.5万
  • 岳荣先 随机伪蒙特卡罗方法的理论与应用3.5万
  • 田红炯 滞时微分动力系统的数值方法3.5万
  • 丛玉豪 常微分数值方法在求解时滞方程及Hamilton系统中的应用3万
  • 徐承龙 金融衍生物的偏微分方程定价及计算3万
  • 王元明 非线性初(边)值问题的高精度有限差分方法3万
  • 王中庆 奇异问题和无界区域问题的谱方法3万
4.特聘研究员承担了18项国家和上海市科研项目,本年度到达的总经费57.9万元。
A.国家科研项目8个,本年度到达经费40.4万元。
  • 程  晋   国家自然科学重点项目《数学物理方程的反问题及其应用》。
  • 程  晋   国家重大基础研究项目《针刺效应与经络功能的科学基础》,数学模型。
  • 程  晋   国家重大基础研究项目《复杂环境时空定量信息获取与融合处理的理论与应用》。
  • 程  晋   国家自然科学基金项目,数学物理反问题的条件稳定性及正则化算法。
  • 郭本瑜   国家自然科学基金项目,奇异问题及非矩形和无界区域问题的谱方法。
  • 黄建国   国家自然科学基金,组合弹性结构动力学问题数值解研究。
  • 王元明   国家自然科学基金,非线性椭圆型边值问题的高精度有限差分方法。
  • 徐承龙   国家自然科学基金,金融衍生物定价问题中的偏微分方程粘性解理论与计算。
B.上海市及教育部科研项目10个,本年度到达经费17.5万元。
  • 郭本瑜   上海市科委重点项目,若干数学物理复杂问题的计算方法。
  • 郭本瑜   国家教育部博士点基金,奇异问题和无界区域问题的谱方法及其应用。
  • 程  晋   教育部新世纪优秀人才计划,数学物理方程反问题及其数值解。
  • 程  晋   国家教育部博士点基金,数学物理反问题。
  • 田红炯   上海市科委启明星计划基金,滞时微分动力系统的数值分析。
  • 田红炯   上海市优秀青年教师后备人选研究基金,中立型微分系统的数值分析。
  • 王中庆   上海市教委科研基金,奇异和无界区域问题的高精度算法。
  • 王元明   上海市教委科研基金,时滞反应扩散方程组数值解的渐近性及其应用。
  • 丛玉豪   上海市教委科研基金,非自治无穷维Hamilton系统的多辛几何算法。
  • 岳荣先   上海市教委科研基金,随机化伪Monte Carlo积分法的易处理性研究。
5.最近申请并获准主持4个国家和上海市科研项目,总经费92万元。这些项目将从2007年开始执行。
  • 田红炯     国家自然科学基金,滞时泛函微分动力系统的计算方法。
  • 田红炯     上海市科委基础研究重点项目,泛函微分动力系统的计算方法及其应用。
  • 田红炯     上海市教委曙光计划,泛函微分动力系统的数值模拟及其应用。
  • 岳荣先     国家自然科学基金项目,高维积分的伪蒙特卡洛算法及其在巴拿赫空间上的误差分析。
 
三、科学研究成果
本年度在奇异和无界区域问题的高精度数值方法、动力系统的数值研究、组合弹性结构的数学模型和计算、随机化伪Monte-Carlo方法及其应用,及数学物理反问题的数值解法等方面取得了一批研究成果,在国内外重要学术刊物上发表了23篇论文,其中某些结果是原创性的。此外,编辑了两本国际会议学术论文集。

1.数学物理问题的高精度算法(郭本瑜,王中庆)
  • 继续发展带权Sobolev空间中Jacobi正交逼近及其插值的基本理论,构造有关高阶、退化问题及非直角区域上谱及拟谱方法,并应用于相关问题的计算。数值结果显示了这些新算法的优越性。
  • 建立了带负参数的Jacobi正交逼近理论,并由此构造了高阶微分方程的谱方法,特别是广义KDV等高奇数阶微分方程的谱方法。
  • 建立了一类新的广义Laguerre正交逼近及其插值的基本理论,并应用于有关退化问题,无界区域及外部问题的计算。数值结果显示了这些新算法的优越性。
  • 继续发展Hermite正交逼近理论,特别是带权 的Hermite正交逼近和插值理论,并应用于无限长条区域上的热传导问题。
有关论文:
[1]Wang Li-lian and Guo Ben-yu, Mixed Fourier-Jacobi spectral method, J. of Math. Anal. and Appl., 315(2006), 8-28.
[2]Guo Ben-yu, Wang Li-lian and Wang Zhong-qing, Generalized Laguerre interpolation and pseudospectral method for unbounded domains, SIAM J. Numer. Anal., 43(2006), 2567-2589.
[3]Guo Ben-yu and Wang Li-lian, Modified Laguerre pseudospectral method refined by multidomain Legendre pseudospectral approximation, J. of Comp. Appl. Math., 190(2006), 304-324.
[4]Ben-yu Guo, Jie Shen and Wang Li-lian, Optimal spectral-Galerkin methods using generalized Jacobi polynomials, J. Sci. Comp., 27(2006), 305-322.
[5]Zhang Xiao-yong and Guo Ben-yu, Spherical harmonic-generalized Laguerre spectral method for exterior problems, J. Sci. Comp., 27(2006), 523-537.
[6]Guo Ben-yu and Wang Tian-jun, Mixed Leguerre-Hermite spectral method for heat transfer in infinite plate, Comp. and Math. with Appl., 51(2006), 751-768.
[7]Wang Li-lian and Guo Ben-yu, Stair pseudospectral method for differential equations on the half line, Adv. in Comp. Math., 25(2006), 305-322.
[8]Zheng-su Wan, Ben-yu Guo and Zhong-qing Wang, Jacobi pseudospectral method for fourth order problems, J. of Comp. Math., 24(2006), 481-500.
[9]Ben-yu Guo and Xiao-yong Zhang, Spectral method for differential equations of degenerate type on unbounded domains by using generalized Laguerre functions, Appl. Numer.Math., DOI:10.1016/j.apnum.2006.07.032, 14 August 2006.

2.动力系统的数值方法(丛玉豪,田红炯)

  • 利用非线性分岔理论给出了伪平衡解和伪周期2解的存在性的统一方法,并研究Runge-Kutta方法和线性多步法求解滞时微分方程的正则性。
  • 研究了线性 方法和线性多步法求解非线性滞时微分方程的非线性耗散性,证明了非线性耗散性与 稳定性的等价性。数值实验的结果验证了理论的正确性。
  • 研究了多滞时中立系统渐近稳定性,给出了一种充分条件。利用这个充分条件,讨论了相应线性多步方法的数值稳定性,证明了一个渐近稳定的充分必要条件。
  • 块θ-方法是一种具有较好稳定性、又不需要使用高阶导数的重要数值方法。研究了应用块θ-方法求解滞时微分方程的数值稳定性,分析了滞时微分方程系统的渐近稳定性,证明了其GP-稳定当且仅当1/2≤θ≤1,GPLm—稳定当且仅当θ=1;同时讨论了将其应用于中立型系统渐近稳定的充分必要条件。
有关论文:
[1]Baker,  Bocharov, Filiz, Ford, Paul, Rihan, Thomas, Tian & Wille, Numerical Modelling by delay and Volterra functional differential equations, in the book Computer Mathematics and its Applications, edited by Professor Elias A. Lipitakis, 2006, 233-256.
[2]H. Tian, L. Fan, Y. Zhang and  J. Xiang, Spurious Numerical Solutions of Delay Differential Equations, J. Comp. Math., 24(2006), 181-192.
[3]Cong Yuhao, Xu Li and Kuang Jiaoxun, The asymptotic stability of numerical methods for the neutral delay differential equations with multiple delay, Journal of system simulation, 18(2006), 3386-3389.

3.组合弹性结构问题的有限元方法(黄建国)

  • 通过建立一个关键恒等式发展了固支边情形TRUNC板元的内蕴误差估计理论,简化了已有结果的证明,并进而获得混合边界条件情形的拟最优误差估计。以此理论为基础,构造了TRUNC型的耦合有限元法求解一般组合弹性结构问题,并建立相应的拟最优误差估计理论,数值模拟结果说明了算法的有效性。
  • 基于一般组合弹性结构问题数学理论的研究成果,建立了求解一般组合弹性结构的一个有限元方法,给出了相应非协调元空间上的Korn不等式,并给出了有限元解在能量模意义下的最优误差估计。
  • 通过利用非规则流形上位势理论,和作者建立的关于变系数情形分片调和函数表示公式及估计,借助于形式渐近分析技巧,获得变系数情形二阶椭圆型方程的显式先验估计,并利用向量场Hodge分解理论,获得静态Maxwell方程组的显式先验估计。
  • 建立了求解Kirchhoff板振动的半离散和全离散格式以及C0连续时间方向Galerkin离散化方法。给出了相应的误差估计和数值模拟结果。
有关论文:
[1]J. Huang, Z. Shi, Y. Xu, Finite element analysis for general elastic multi-structures, Science in China Ser. A, 49(2006), 109-129.
[2]L. Guo, J. Huang, and Z. Shi, Remarks on error estimates for the TRUNC plate element, Journal of Computational Mathematics, 24(2006), 103-112.
[3]J. Huang and J. Zou, Uniform a priori estimates for elliptic and static Maxwell interface problems, Discrete and Continuous Dynamical Systems Ser. B, 7(2007), 145-170. (电子版2006年已发表)。

4.金融衍生物的偏微分方程定价及计算(徐承龙)
  • 对一类累积型的金融衍生产品建立了数学定价模型,并求出了定价公式。阐明了产品的价格与各相关金融参数的相互关系。
  • 对一类金融衍生产品的数学模型提出了区域分解的Laguerre谱-差分方法,构造了相应的基函数,并进行了数值计算和理论分析。
  • 对我国金融市场中的一类可调转股价的可转债建立了定价模型,用二叉树方法进行了计算,并讨论了可转债定价机制。对我国的金融市场中可转债的发行有一定的参考意义。
有关论文:
[1]林颖,徐承龙,一种累积型理财产品的定价分析,现代管理科学,154(2006), 103-104.
[2]徐承龙,谢志华,一类可调转股价可转债的定价分析与计算,高等学校计算数学学报,27(2006), 127-131.

5.非线性初(边)值问题的高精度有限差分方法(王元明)
  • 研究了一类非线性时滞反应扩散方程组的差分方法,构造了相应的单调迭代解法,该算法不需要非线性反应函数的任何单调性。讨论了数值解的渐近收敛性,包括局部或整体吸因子。对一个酶反应扩散问题给出了具体的应用和一些数值结果。又对非线性抛物型方程组建立了在时间和空间方向上具有高阶精度的单调紧致差分格式,该格式还保持了原问题的一些性质。
  • 对一类非线性时滞反应扩散方程数值解和一类互助型反应扩散模型解的渐近收敛性给出了定性刻划。这些结果反应了生物模型的共存性、持久性和消失性,对研究不同物种的共存性及逗留性有一定的指导意义。
  • 对一类非线性两点边值问题构造了一种具有四阶精度的有限差分方法。对Numerov 格式的数值解给出了渐近误差展开式,在此基础上建立了Numerov 格式的外推算法,改进了数值解的精度。又对非线性椭圆边值问题有限差分解的计算建立了具有二次收敛率的单调迭代算法。
有关论文:
[1]Yuan-Ming Wang, Convergence analysis of monotone method for fourth-order semilinear elliptic boundary value problems, Appl. Math. Letters, 19(2006), 332-339.
[2]Yuan-Ming Wang, Asymptotic behavior of solutions for a cooperation-diffusion model with a saturating interaction, Computers Math. Applic., 52(2006), 339-350.
[3]Yuan-Ming Wang and C.V. Pao, Time-delayed finite difference reaction-diffusion systems with nonquasimonotone functions, Numer. Math., 103(2006),485-513.

6.随机伪蒙特卡罗方法的理论与应用(岳荣先)

  • 研究了基于一类 -网格与 -序列的伪Monte Carlo求积法在加权Banach函数空间与有限阶加权的Banach空间中单位球上的极端误差与结点个数及初始误差之间的关系,寻求这类伪Monte Carlo求积法具有易处理性的条件,即研究要使积分误差不超过初始误差的 倍( )的最小的函数计值次数n由维数s与 的多项式而决定,那么加权系数应满足何种条件。
  • 研究了基于一类随机化 -网格与随机化 -序列的随机化伪Monte Carlo求积法在加权Banach函数空间与有限阶加权的Banach空间中单位球上的极端均方误差与结点个数及初始误差之间的关系,寻求这类随机化伪Monte Carlo求积法具有易处理性的条件。
有关论文:
[1]R.X.Yue and F.J. Hickernell, Strong Tractability of Quasi-Monte Carlo Quadrature Using Nets for Certain Banach Spaces, SIAM Journal on Numerical Analysis (2006) 已接受.

7.数学物理反问题的理论和数值方法(程晋)
  • 研究了在更加符合实际问题的假设下的MEG/EEG问题的唯一性问题。
  • 利用正则化方法讨论了高阶数值微分的计算问题。
有关论文:
[1]L. Peng, J. Cheng & L Jin, The unique determination of the primary current by MEG and EEG., Physics Medicine and Biology, 51(2006) 5565-5580.
[2]Y. B. Wang, Y. C. Hon & J. Cheng, Reconstruction of high order derivatives from input data, Journal of Inverse and Ill-Posed Problems, 14(2006), 205-218.
四、学术活动
遵循研究院管理章程进行日常学术活动,并举办或合办了一些国内或国际学术会议。
1.日常学术活动
  • 每月召开全体特聘研究员工作会议,相互交流科学研究工作并部署下一步研究工作。
  • 每月举办一次面向全市的学术报告会,由特聘研究员或院外专家介绍科学计算的新进展。
  • 邀请20名国内、外专家来研究院讲学或合作研究。
  • 研究院7位成员参加了国际学术会议,共8人次,并作邀请报告或报告。多名研究员到国外或境外讲学或短期合作研究。
2.举办或合办国内、外学术会议
  • 2006年5月,   举办动力系统及数值模拟国际学术会议,参加者约100人。
  • 2006年5月,   参加组办应用国际数学论坛,参加者约200人。
  • 2006年12月,  举办上海市第二次科学与工程计算研讨会,参加者约230人。

3.拟办的学术会议
  • 2007年1月,   参加举办第88期上海东方论坛—纳米光学数学和计算的挑战
  • 和机遇。
  • 2007年6月,   谱方法与高阶元方法讨论会。

五、学科建设和人才培养
根据上海高校E—研究院的建设宗旨,加速培养上海市各高校计算数学专业的学术带头人和高水平专业人才,促进有关高校计算数学学科的建设。
1.上海四所大学的计算数学博士点被评为全国前20名。
2.程晋教授获2006年宝钢教育奖,田红炯教授被评为上海市教委曙光计划资助学者。
3.研究院成员共指导了13名博士生(其中毕业1名),和37名硕士生(其中毕业10名),指导国内访问学者2名。黄建国教授指导的一名博士后出站。
4.程晋教授指导的一名博士生获得2006年上海市优秀博士论文奖。

六、工作环境及实验室建设
按计划完成了工作环境及实验室建设。SGI-300高性能工作站扩能工作(由市教委重点学科《计算数学》经费支出)。扩能后达到16G内存,32个CPU。

七、2006年论文摘要
Asymptotic stability of numerical methods for neutral delay differential equations with multiple delays
Y. Cong, L. Xu and J. Kuang
J. System Simulation 18(2006), 3387-3389,3406.
Abstract
The sufficient condition which analytic solution of neutral delay differential equations with multiple delays is asymptotically stable was given; the asymptotic stability of linear multistep methods for the numerical solution of neutral delay differential equations with multiple delays was discussed. By Lagrange Interpolation, it is shown that linear multistep methods are asymptotically stable if and only if it is A-stable.

Modified Laguerre pseudospectral method refined by multidomain Legendre pseudospectral approximation
B. Guo and L. Wang
J. Comp. Appl. Math. 190(2006), 304-324.
Abstract
A modified Laguerre pseudospectral method is proposed for differential equations on the half line. The numerical solutions are refined by multidomain Legendre  pseudospectral approximation. Numerical results show the spectral accuracy of this approach. Some approximation results on the modified Laguerre and Legendre interpolations are established. The convergence of proposed method is proved.

Optimal spectral-Galerkin methods using
generalized Jacobi polynomials
B. Guo, J. Shen  and L. Wang
J. Sci. Comp. 27(2006), 305-322.
Abstract
We extend the definition of the classical Jacobi polynomials with indexes   to allow   and   to be negative integers. We show that the generalized Jacobi polynomials, with indexes corresponding to the number of boundary conditions in a given partial differential equation, are the natural basis functions for the spectral approximation of this partial differential equation. Moreover, the use of generalized Jacobi polynomials leads to much simplified analysis, more precise error estimates and well conditioned algorithms.

Generalized Laguerre interpolation and pseudospectral method for unbounded domains
B. Guo, L. Wang and Z. Wang
SIAM J. Numer. Anal. 43(2006), 2567-2589.
Abstract
In this paper, error estimates for generalized Laguerre-Gauss-type interpolations are derived in non-uniformly Sobolev spaces weighted with  Generalized Laguerre pseudospectral methods are analyzed and implemented. Two model problems are considered. The proposed schemes keep spectral accuracy, and with suitable choice of basis functions, lead to sparse and symmetric linear systems.

Mixed Leguerre-Hermite spectral method
for heat transfer in infinite plate
 B. Guo and T. Wang
Comp. Math. Appl. 51(2006), 751-768.
 Abstract
Non-isotropic heat transfer in an infinite plate is considered. A weak formulation is derived, which is appropriate for its numerical simulation.  Mixed Legendre-Hermite spectral method is proposed for this problem. Its convergence is proved. Numerical results show the efficiency of this new approach.

Remarks on error estimates for the TRUNC plate element
L. Guo, J. Huang and Z. Shi
J. Comp. Math. 24(2006), 103-112.
 Abstract
This paper provides a simplified derivation for error estimates of the TRUNC plate element. The error analysis for the problem with mixed boundary conditions is also discussed.

Finite element analysis for general elastic multi-structures
J. Huang, Z. Shi and Y. Xu
Science in China 49(2006), 109-129.
Abstract
A finite element method is introduced to solve the general elastic multi-structure problem, in which the displacements on bodies, the longitudinal displacements on plates and the longitudinal displacements on beams are discretized using conforming linear elements, the rotational angles on beams are discretized using conforming elements of second order, the transverse displacements on plates and beams are discretized by the Morley elements and the Hermite elements of third order, respectively. The generalized Korn's inequality is established on related nonconforming element spaces, which implies the unique solvability of the finite element method. Finally, the optimal error estimate in the energy norm is derived for the method.

The unique determination of the primary current by MEG and EEG
L. Peng, J. Cheng and J. Lu
Phys. Med. Biol. 51(2006), 5565-5580.
Abstract
In this paper, we use a more realistic head model with ovoid geometry for approximation of a human head. By inverting the Geselowitz equation, some analytic results on the inverse MEG problem are presented in homogenous ovoid geometry. On one hand, some information about the components of primary current is shown by the decomposition of primary current in different coordinates in the case of a special MEG sensor position. On the other hand, in the general case, using decomposition of the primary current in spherical coordinates, we show that two scalar functions which specify the tangential part of the primary current can be uniquely determined with the assumption that two scalar functions are conjugate and harmonic in terms of two variables. Hence, the tangential part of the current can be completely known from the two scalar functions. Moreover, we obtain the unique determination of the primary current by combining MEG and EEG.

Spurious numerical solutions of delay differential equations
H. Tian, L. Fan, Z. Yuan and J. Xiang
J. Comp. Math. 24(2006), 181-192.
Abstract
This paper deals with the relationship between asymptotic behavior of the numerical solution and that of the true solution itself for fixed step-sizes. The numerical solution is viewed as a dynamicalsystem in which the step-size acts as a parameter. We present a unified approach to look for bifurcations from the steady solutions into spurious solutions as step-size varies.

Jacobi pseudospectral method for fourth order problems
Z. Wan, B. Guo and Z. Wang
J. Comp. Math. 24(2006), 481-500.
Abstract
In this paper, we investigate Jacobi pseudospectral method for fourth order problems. We establish some basic results on the Jacobi-Gauss-type interpolations in non-uniformly weighted Sobolev spaces, which serve as important tools in analysis of numerical quadratures, and numerical methods of differential and integral equations. Then we propose Jacobi pseudospectral schemes for several singular problems and multiple-dimensional problems of fourth order. Numerical results demonstrate the spectral accuracy of these schemes, and coincide well with theoretical analysis.

Stair Laguerre pseudospectral method for differential
equations on the half line
L. Wang and B. Guo
Adv. Comp. Math. 25(2006), 305-322.
Abstract
A stair Laguerre pseudospectral method is proposed for numerical solutions of differential equations on the half line. Some approximation results are established. A stair Laguerre pseudospcetral scheme is constructed for a model problem. The convergence is proved. The numerical results show that this new method provides much more accurate numerical results than the standard Laguerre spectral method.

Mixed Fourier-Jacobi spectral method
L. Wang and B. Guo
J. Math. Anal. Appl. 315(2006), 8-28.
Abstract
This paper is for mixed Fourier-Jacobi approximation and its applications to numerical solutions of semi-periodic singular problems, semi-periodic problems on unbounded domains and axisymmetric domains, and exterior problems. The stability and convergence of proposed spectral schemes are proved. Numerical results demonstrate the efficiency of this new approach.


Reconstruction of high order derivatives from input data
Y. Wang, Y. Hon and J. Cheng
J. Inv. Ill-Posed Problems 14(2006), 205-218.
Abstract
This paper gives a numerical method for reconstructing the original function and its derivatives from discrete input data. It is well known that this problem is ill-posed in the sense of Hadamard. The solution for the first order derivative has been proposed by [10] and [17], using the Tikhonov regularization technique. In this paper, under an assumption that the original function has a square integrable k-th order derivative, we propose a reconstruction method for the j-th order derivative where  . A convergence rate estimate is obtained by taking a new choice of the Tikhonov parameter. Numerical example is given to verify the effectiveness and accuracy of the proposed method.

Asymptotic behavior of solutions for a Cooperation-Diffusion model with a Saturating interaction
Y. Wang
Comp. Math. Appl. 52(2006), 339-350.
Abstract
This paper is concerned with a Lotka-Volterra cooperation-diffusion model with a saturating interaction term for one species. The goal of the paper is to investigate the asymptotic behavior of the time-dependent solution in relation to the corresponding steady-state solutions under homogeneous Neumann boundary condition. Some simple and easily verifiable conditions are given to the rate constants so that for every nontrivial nonnegative initial function the corresponding time-dependent solution converges to one of the nonnegative constant steady-state solutions as time tends to infinity. This convergence result leads to the existence and uniqueness of a positive (or nonnegative) steady-state solution and the global asymptotic stability of a given nonnegative constant steady-state solution. In terms of ecological dynamics, it also gives some coexistence, permanence and extinction results for the model.

Convergence analysis of a monotone method for fourth-order semilinear elliptic boundary value problems
Y. Wang
Appl. Math. Lett. 19(2006), 332-339.
Abstract
This work is concerned with the convergence of a monotone method for fourth-order semilinear elliptic boundary value problems. A comparison result for the rate of convergence is given. The global error is analyzed, and some sufficient conditions are formulated for guaranteeing a geometric rate of convergence.

Time-delayed finite difference Reaction-Diffusion systems with nonquasimonotone functions
Y. Wang and C.V. Pao
Numer. Math. 103(2006), 332-339.
Abstract
This paper is concerned with finite difference solutions of a system of reaction-diffusion equations with coupled nonlinear boundary conditions and time delays. The reaction functions and the boundary functions are not necessarily quasimonotone, and the time delays may appear in the reaction functions as well as in the boundary functions. The investigation is devoted to the finite difference system for both the time-dependent problem and its corresponding steady-state problem. Some monotone iteration processes for the finite difference systems are given, and the asymptotic behavior of the time-dependent solution in relation to the steady-state solution is discussed. The asymptotic behavior result leads to some local and global attractors of the time-dependent problem, including the convergence of the time-dependent solution to a unique steady-state solution. An application and some numerical results to an enzyme-substrate reaction-diffusion problem are given. All the results are directly applicable to parabolic-ordinary systems and to reaction-diffusion systems without time delays.

A mixed spectral method for incompressible viscous fluid flow in an
infinite strip
Z. Wang and B. Guo
Comp. Appl. Math. 27(2005),343-364.
Abstract
This paper considers the numerical simulation of incompressible viscous fluid flow in an infinite strip. A mixed spectral method is proposed using the Legendre approximation in one direction and the Legendre rational approximation in another direction. Numerical results demonstrate the efficiency of this approach. Some results on the mixed Legendre-Legendre rational approximation are established, from which the stability and convergence of proposed method follow.

Error analysis on scrambled Quasi-Monte Carlo quadrature rules using Sobol points
R. Yue
Frontiers and Contemporary Applied Mathematics, CAM 6, 2005, 254-267.
Abstract
We study the worst-case error and random-case of scrambled Quasi-Monte Carlo quadrature rules using Sobol points. The function spaces considered in this article are the weighted Hilbert spaces  generated by Haar wavelets with weights  and a parameter  which reflects the smoothness of the spaces. Conditions are found under which multivariate integration using the scrambled Sobol points is strongly tractable in the worst-case and random-case settings, respectively. The worst-case results improve upon those of Wang (2003). The random-case results give weaker conditions for strong tractability than in the worst-case setting.

Spherical harmonic-generalized Laguerre spectral method
for exterior problems
 X. Zhang and B. Guo
J. Sci. Comp. 27(2006), 523-537.
Abstract
In this paper, we propose the mixed spherical harmonic-generalized Laguerre spectral method for three-dimensional exterior problems. Some approximation results are established. As an example, a model problem is considered. The convergence of proposed scheme is proved. Numerical results demonstrate the efficiency of this approach.

发布者: eicssu admin
发布日期: 12/31/2006
浏览次数: 1333

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