二维线性常系数Schrdinger方程的两个ADI格式

在量子力学、等离子物理等许多学科中,均有大量的Schrdinger型方程,其数值求解具有重要的物理意义。本文提出了数值求解二维线性常系数Schrdinger方程的两个ADI格式(P—R格式和M—F格式),通过Von-Neumann方法判断出这两个格式均是无条件稳定的。运用Taylor展开,得出这两个格式在点处的截断误差分别为O(k2+h2)和O(k2+h4)。数值实验中,固定h,变动k,画出每次的误差曲线,验证了该格式的无条件稳定性;数值实验还表明,用这两个交替方向隐格式计算比用通常的C-N格式所消耗的CPU时间大大减少,因而该格式具有一定的实际意义。     

一种求解一维对流扩散方程的高精度紧致隐式差分格式

提出了数值求解一维非定常对流扩散方程的一种两层四阶紧致隐式差分格式,其截断误差为O（τ^2＋h^4）.采用von Neumann方法证明了格式是无条件稳定的,并且由于每一时间层上只用到了3个网格点,所以可直接采用追赶法求解差分方程.数值实验结果验证了该方法的精确性和可靠性.     

求解扩散方程的一种高精度隐式差分方法

利用一阶微商和二阶微商的四阶紧致差分逼近公式,推导出了数值求解一维扩散方程的两种新的高精度隐式紧致差分格式,其截断误差分别为O(τ^2 h^4)和O(τ^4 h^4)．通过Fourier分析方法证明了格式O(τ^2 h^4)是无条件稳定的,而格式O(r^4 h^4)是无条件不稳定的．并且由于每一时间层上只用到了3个网格点,所以差分方程可采用追赶法直接进行求解．     

求解二维扩散方程的加权平均隐式多重网格方法

提出了数值求解二维扩散方程两种精度分别为O(τ^2 h^2)和O(τ^2 h^4)的无条件稳定的加权平均隐格式，并采用多重网格方法进行求解，从而克服了传统迭代法在求解隐格式时收敛速度慢的缺陷，提高了求解效率．数值实验验证了该方法的精确性和可靠性．     

三维波动方程的隐式多重网格方法

提出了数值求解三维波动方程的两种精度分别为O(τ^2 h^2)和O(τ h^4)的三层紧致隐格式,利用Fourier分析方法证明了格式均是无条件稳定的．并在此基础上提出了求解该问题的多重网格算法,从而克服了传统迭代法在求解隐格式时收敛速度慢的缺陷,大大加快了迭代收敛速度,提高了求解效率．数值实验结果验证了方法的精确性和可靠性．     

求解波动方程的高精度紧致隐式差分方法

基于二阶微商的二阶中心差商和四阶紧致差商逼近公式及其加权平均思想,推导出了数值求解一维波动方程的2种精度分别为O（x^2＋h^4）和O（x^4＋h^4）的三层隐式紧致差分格式,以夏与之相匹配的第一个时间步的同阶离散格式,并采用Fourier方法分析了格式的稳定性．由于每一时间层上最多只用到了3个网格点,所以可采用追赶法直接求解差分方程．数值实验结果验证了所得方法的精确性和可靠性．     

求解热传导方程的Crank-Nicolson方法

给出了数值求解热传导方程的一种Crank-Nicolson格式,其截断误差为O（τ^2＋h^2）,并且分析了该差分格式的稳定性.在最后的数值例子中,验证了该格式求解出的数值解可以很好的逼近精确解,以及当空间步长和时间步长同时缩小1/2倍时,最大误差约缩小为原来的1/4.     

非球谐环形振子势的Schrdinger方程的解析解

量子力学中除了无限深势阱、一维线性谐振子、库仑势和三维各向同性谐振子势外,绝大部分Schrodinger方程是没有精确解的,这给具体问题的深入研究带来了很大的障碍。本文从求解Schrodinger方程的NU Method方法出发,求解了非球谐环形振子势V（r,θ）=μω^2r^2／2＋h^2α／（2μr^2）＋h^2βcosθ／（2μr^2sinθ）的本征方程的角向方程,获得解析解,将求解的过程大大简化;同时用特殊函数的方法求解了非球谐环形振子势的Schodinger方程的径向方程,借以拓宽对Schrodinger方程求解方法的研究。     

一类拟线性神经传播方程的紧LOD差分格式

通过引入变量将方程从形式上降阶,提出了求解一类拟线性神经传播方程的紧局部一维（LOD）差分格式,并应用能量方法给出了格式的误差估计,得到该格式在L^2模下具有O（Δt^2＋h^4）的精度．最后通过数值例子验证了算法的有效性．     

色散方程的两个隐式差分格式

给出了色散方程的两个隐式差分格式,其截断误差均为0（τ＋h^2）,其中一个格式是无条件稳定的．     

Markedness and its Interpretation in Language Use

Language markedness is a common phenomenon in languages, and is reflected from hearing, vision and sense, i.e. the variation in the three aspects such as phonology, morphology and semantics. This paper focuses on the interpretation of markedness in language use following the three perspectives, i.e. pragmatic interpretation, psychological interpretation and cognitive interpretation, with an aim to define the function of markedness.     

Features of Women's language

Language is a means of verbal communication. People use language to communicate with each other. In the society, no two speakers are exactly alike in the way of speaking. Some differences are due to age, gender, statue and personality. Above all, gender is one of the obvious reasons. The writer of this paper tries to describe the features of women＇s language from these perspectives： pronunciation, intonation, diction, subjects, grammar and discourse. From the discussion of the features of women＇s language, more attention should be paid to language use in social context. What＇s more, the linguistic phenomena in a speaking community can be understood more thoroughly.     

低渗透非均质砂岩油藏启动压力梯度研究

理论推导与室内实验相结合,建立了低渗透非均质砂岩油藏启动压力梯度确定方法。首先借助油藏流场与电场相似的原理,推导了非均质砂岩油藏启动压力梯度计算公式。其次基于稳定流实验方法,建立了非均质砂岩油藏启动压力梯度测试方法。结果表明:低渗透非均质砂岩油藏的启动压力梯度确定遵循两个等效原则。平面非均质油藏的启动压力梯度等于各级渗透率段的启动压力梯度关于长度的加权平均;纵向非均质油藏的启动压力梯度等于各渗透率层的启动压力梯度关于渗透率与渗流面积乘积的加权平均。研究成果可用于有效指导低渗透非均质砂岩油藏的合理井距确定,促进该类油藏的高效开发。     

On Tragic Consciousness In The Works By Ernest Hemingway

As an American modern novelist who were famous in the literary world, Hemingway was not a person who always followed the trend but a sharp observer. At the same time, he was a tragedy maestro, he paid great attention on existence, fate and end-result. The dramatis personae's tragedy of his works was an extreme limit by all means tragedy on the meaning of fearless challenge that failed. The beauty of tragedy was not produced on the destruction of life, but now this kind of value was in the impact activity. They performed for the reader about the tragedy on challenging for the limit and the death.     

Achieving Unusual States of Matter Under High Pressure

正The periodicity of the elements and the non-reactivity of the inner-shell electrons are two related principles of chemistry,rooted in the atomic shell structure.Within compounds,Group I elements,for example,invariably assume the+1 oxidation state,and their chemical properties differ completely from those of the p-block elements.These general rules govern our understanding of chemical structures and reactions.Using first principles calcula-     

Exchange-Correlation and Electronic Excitation Energies from Pairing Matrix Fluctuations

We have developed an adiabatic connection to formulate the ground-state exchange-correlation energy in terms of pairing matrix linear fluctuations.This formulation of the exchange-correlation energy opens a new channel for density functional approximations based on the many-body perturbation theory.We illustrate the potential of such approaches with an approximation based on the particle-particle Random Phase Approximation(pp-RPA).This re-     

Density Functional Theory for the Response of Periodic Systems to Electric Fields Based on the Vector Potential Approach

正The electronic and nuclear(structural/vibrational)response of 1D-3D nanoscale systems to electric fields gives rise to a host of optical,mechanical,spectral,etc.properties that are of high theoretical and applied interest.Due to the computational difficulty of treating such large systems it is convenient to model them as infinite and periodic(at least,in first approximation).The fundamental theoretical/computational problem in doing so is that     

On the Thermodynamic Limit for Responses to Static Electromagnetic Fields

For molecular systems,the quantum-mechanical treatment of their responses to static electromagnetic fields usually employs a scalar-potential treatment of the electric field and a vector-potential treatment of the magnetic field.Although the potential for each field separately is associated with the choice of an(unphysical)origin,the precise choice of the origin for the electrostatic field has little consequences for the results.This is different for the     

Call for Papers

<正>"The Journal of Shanghai Normal University:Mathematics"is published by Shanghai Normal University as regular issues of The Journal of Shanghai Normal University each year from 2014 in English.The editors-in-chief of the issues are professors Yuhao Cong and Maoan Han.The Journal of Shanghai Normal University was started in 1958 with     

Journal of Donghua University ( English Edition) Contents of Volume 31

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