求解对流扩散方程的紧致差分方法

首先将指数变换u=pexpk2ε{x}以及降阶法和降维法相结合对常系数对流扩散方程构造了新的紧差分格式,给出了差分格式截断误差的表达式;并利用Fourier稳定性方法证明了该格式的稳定性,且收敛阶为O(τ2+h4).其次应用Richardson外推法对该紧差分格式外推一次得到O(τ4+h6)阶精度的近似解,最后通过数值算例说明该格式的有效性.     

三维抛物型方程的紧交替方向差分格式

对三维抛物型方程构造了一个高精度恒稳定的紧交替方向差分格式,格式的截断误差阶为O(Τ2+h4).然后,将Richardson外推法应用于所构造的格式,得到了具有0(τ3+h6)阶精度的近似解.     

二维抛物型方程的高稳定性两层显式格式

利用加耗散项的方法,通过选取适当参数,构造二维抛物型方程的若干两层显式差分格式.其局部截断误差阶为O(τ h2),而稳定性条件最好为r=(Δt)/((Δx)2)=(Δt)/((Δy)2)=(τ)/(h2)≤1,优于(或不亚于)其他两层显格式,且这些格式都是简洁实用的两层显格式.数值试验表明,所做的稳定性分析是正确的.     

求解一维抛物型方程的一种高精度半显式差分方法

利用加权平均思想和二阶微商的四阶紧致差分逼近公式,构造了一种求解一维抛物型方程的高精度半显式差分格式,其截断误差为O(τ2 h4).通过Fourier分析方法证明了该格式是无条件稳定的.通过数值算例验证了本文方法的精确性和可靠性.     

解Schrodinger方程的高精度外推差分格式

通过构造Schrodinger方程的Crank-Nicolson格式,再利用Richardson外推法得到了一种高精度差分格式,这种格式具有O(τ4+h4)阶精度,且是无条件稳定的.数值算例表明,该算法比古典Crank-Nicolson格式精度更高.     

正则长波方程的一个新的差分逼近

考虑具有齐次边界条件的正则长波方程的有限差分方法,构造了一个3层非线性的隐式差分格式,该格式合理地模拟了初边值问题的守恒性质,得到了差分解的先验估计,并利用离散泛函分析方法分析了该格式的收敛性与无条件稳定性,从理论上得到了收敛的阶为O(τ2+h2).数值实验表明,该方法是可信的.     

解四阶抛物型方程的高精度显式差分格式

对四阶抛物型方程ut+uxxxx=0,构造一个新的三层显式差分格式,其稳定性条件和局部截断误差阶分别为r=τ/h4≤1/8和O(2τ+h6),其结果优于其他四阶抛物型方程的结果.数值例子表明,理论分析是正确的,该格式是有效的.     

求解扩散方程的二级四阶隐式Runge-Kutta方法

对空间变量应用中心差分格式和紧致差分格式离散,时间变量采用二级四阶Runge-Kutta方法,构造求解扩散方程的精度为O(τ4+h2)和O(τ4+h4)的两种绝对稳定的隐式差分格式,讨论稳定性,并将数值试验结果与CrankNicholson格式进行比较,数值结果表明该方法是求解扩散方程的有效数值计算方法之一.     

多项式拟合数值边界格式及其稳定性分析

根据构造无反射数值边界格式的基本思想,采用多项式拟合的方法,构造了一种高精度的数值边界格式(SFEBS).理论分析表明:SFEBS边界格式与4阶紧致差分格式相结合,既能保持格式的G-K-S稳定性,又能保持三对角矩阵是严格对角占优的.数值试验表明:2阶和3阶边界格式分别能够保持3阶和4阶的整体精度;4阶的SFEBS格式也能够保持4阶的整体精度,同时能够减小自由流出边界上的最大误差.     

一类非线性Sobolev-Galpern型湿气迁移方程双线性元的超收敛和外推

主要讨论了一类非线性Sobolev-Galpern型湿气迁移方程的双线性元逼近,利用积分恒等式和平均值技巧,导出了H1模意义下O(h2)阶的超逼近性质.同时借助于插值后处理技术,给出了整体超收敛结果.在此基础上,通过构造合适的外推格式,得到了具有O(h3)阶的近似解.     

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     

An affordable accurate evaluation of the binding conformations predicted by molecular docking studies in bio-system

Franck-Condon factors bridge the gap between theoretical modeling and experimental observations for molecular electronic spectroscopy and electron transfer.Under the displaced harmonic oscillator approximation,multidimensional Franck-Condon factors are decomposed into a product of many one-dimensional(1D)Franck-Condon(FC)factors,and each 1D-FC factor is associated with one Huang-Rhys factor that determines the leading contribution of     

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