ON THE LOCAL WELL-POSEDNESS FOR THE DUMBBELL MODEL OF POLYMERIC FLUIDS

In this paper, we consider the local well-posedness of smooth solutions to a coupled microscopic-macroscopic model for polymeric fluid in general space dimension and with general initial data in Holder space.     

三维血吸虫病模型的离散算子数值解法及理论分析

本文基于积分守恒性质,应用离散算子方法,给出了三维血吸虫病模型第一齐次边值问题的离散格式,同时证明了数值解的非负性和有界性,较好地体现了这一问题的实际背景,另外给出了最优L~2模误差估计。     

THEORETICAL AND NUMERICAL STUDY OF THE BLOW UP IN A NONLINEAR VISCOELASTIC PROBLEM WITH VARIABLE-EXPONENT AND ARBITRARY POSITIVE ENERGY

In this paper,we consider the following nonlinear viscoelastic wave equation with variable exponents:■,where μ is a nonnegative constant and the exponent of nonlinearity p(·) and g are given functions.Under arbitrary positive initial energy and specific conditions on the relaxation function g,we prove a finite-time blow-up result.We also give some numerical applications to illustrate our theoretical results.     

河流分类的灰色理论模型

根据灰色关联度的定义，运用加权广义距离构造目标函数，建立了一种灰色综合评判理论模型．应用该模型对辽宁省15条河流进行了综合评价，结果表明该模型分辨率高、可靠性强，并且具有数学推导严谨、科学合理等特点．     

A NUMERICAL STUDY FOR THE PERFORMANCE OF THE WENO SCHEMES BASED ON DIFFERENT NUMERICAL FLUXES FOR THE SHALLOW WATER EQUATIONS

In this paper we investigate the performance of the weighted essential non-oscillatory （WENO） methods based on different numerical fluxes, with the objective of obtaining better performance for the shallow water equations by choosing suitable numerical fluxes. We consider six numerical fluxes, i.e., Lax-Friedrichs, local Lax-Friedrichs, Engquist-Osher, Harten-Lax-van Leer, HLLC and the first-order centered fluxes, with the WENO finite volume method and TVD Runge-Kutta time discretization for the shallow water equations. The detailed numerical study is performed for both one-dimensional and two-dimensional shallow water equations by addressing the property, and resolution of discontinuities. issues of CPU cost, accuracy, non-oscillatory     

A NUMERICAL STUDY OF THE GAUSSIAN BEAM METHODS FOR SCHRODINGER-POISSON EQUATIONS

As an important model in quantum semiconductor devices, the SchrSdinger-Poisson equations have generated widespread interests in both analysis and numerical simulations in recent years. In this paper, we present Gaussian beam methods for the numerical simulation of the one-dimensional Schrodinger-Poisson equations. The Gaussian beam methods for high frequency waves outperform the geometrical optics method in that the former are accurate even around caustics. The purposes of the paper are first to develop the Gaussian beam methods, based on our previous methods for the linear SchrSdinger equation, for the Schrodinger-Poisson equations, and then check their validity for this weakly-nonlinear system.     

DEPENDENCE OF QUALITATIVE BEHAVIOR OF THE NUMERICAL SOLUTIONS ON THE IGNITION TEMPERATURE FOR A COMBUSTION MODEL

We study the dependence of qualitative behavior of the numerical solutions （obtained by a projective and upwind finite difference scheme） on the ignition temperature for a combustion model problem with general initial condition. Convergence to weak solution is proved under the Courant-Friedrichs-Lewy condition. Some condition on the ignition temperature is given to guarantee the solution containing a strong detonation wave or a weak detonation wave. Finally, we give some numerical examples which show that a strong detonation wave can be transformed to a weak detonation wave under some well-chosen ignition temperature.     

A NUMERICAL METHOD OF THE EIGENVALUES AND THE EIGENVECTORS FOR ANTI-SYMMETRIC TRIDIAGONAL MATRIX

1 The principal conclusionTh1:For every anti-symmetric tridiagonal n×n matrix A with the off-diagonal ele-ments±β_i(i=1,2,…n-1),there is an orthogonal matrix L such thatLA~TAL~T=(?)(C and D is all symmetric tridiagonal matrix).And the elements c_(ij),d_(ij)and l_(ij)of matrix C,D and L are determined by the followng meth-     

分数阶微分方程的理论和数值方法研究

分数阶偏微分方程的研究有很长的历史,并在最近十多年得到快速发展.相比极为有限的理论成果,数值方法的研究成果已经相当丰富,几个国际研究团队对此作出了贡献.本文旨在对分数阶微分方程的理论与数值方法研究成果做个简要的评价,聚焦总结评述与高阶方法发展密切相关的研究.主要内容为讨论最基本的三类方程:时间分数阶扩散方程、空间分数阶扩散方程、以及时空分数阶扩散方程的理论进展和数值方法研究在最近十年取得的结果.我们还有针对性地选择一些算例,用以说明几个重要方法的精度和有效性.     

统计力学格点模型的数值方法

相变是自然界普遍发生的一种突变现象.自上一世纪以来,这一现象的研究便引起了科学工作者的极大注意,其焦点集中在诸如气-液相变、铁磁性相变等与临界点有关的现象上. 当一个系统经受相变时,描述系统状态的某些物理量会产生奇性,这种现象是与微观粒子间的相互作用和热运动二者密切相关的.然而试图利用数学物理的方法,对相变现     

数值模拟混溶驱动问题的迎风格式及理论分析

本文提出数据模拟混溶驱动问题的一类广义迎风格式，严格证明了其满足离散极值原理和离散质量守恒原理，并获得收敛性定理，对模型问题的试算，得到令人满意的数值结果。     

哮喘模型的谱方法与逆谱方法

哮喘模型的谱方法与逆谱方法鲁百年（陕西师范大学数学系）ＳＰＥＣＴＲＡＬＡＮＤＰＳＥＵＤＯＳＰＥＣＴＲＡＬＡＰＰＲＯＸＩＭＡＴＩＯＮＳＦＯＲＴＨＥＭＯＤＥＬＯＦＷＨＥＥＺＥＳ￥ＬｕＢａｉ－ｍｉａｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｓｈａ...     

认股权证的等价鞅测度定价模型与数值方法

本文对认股权证应用等价鞅测度方法进行定价 .推导出计算更自然、更简单的类似 Black- Scholes模型的认股权证定价公式 .给出了一种比较好的数值计算方法 .并讨论了认股权证在中国证券市场的发展状况 .     

依赖个体尺度结构的种群资源开发模型理论分析

研究一类具有个体尺度结构的非线性种群控制模型.确立了状态系统模型非负解的存在唯一性,以及状态关于控制变量的连续依赖性.应用紧性推理和极值化序列法证明了最优策略的存在性,借助切锥法锥和共轭系统技巧导出了最优性条件.     

一个淋病扩散模型的定性分析

本文利用奇点理论与Ｂｅｎｄｉｘｓｏｎ定理对淋病扩散模型进行了定性分析,给出了可行平衡点附近,特别是高阶平衡点附近轨线的定性结构,研究了可行平衡点的全局渐近稳定性,得到了完整的结果。     

基于残差平方和的线性模型选择简单方法及其相合性研究

本文研究了回归分析理论中的自变量选择的重要问题,利用线性回归模型自变量增减的残差平方和理论,获得了一种选择自变量的准则,该准则的分析表明,它计算简单,而且在一定的条件下具有强相合性.