抛物型方程的一个高精度隐格式

利用待定参数法,对一维抛物型方程构造出了一个截断误差为Ｏ（△ｘ＾４＋△ｘ＾４）的隐式差分格式,格式的稳定性条件为ｒ＝ａ△ｔ／△ｘ＾２≤１／√２,可用追赶法求解。     

解高维热传导方程的一个高精度ADI格式

构造了一个解四维热传导方程的一个高精度ADI格式,格式绝对稳定,截断误差阶达到O(△t~2 △x~4).可用追赶法求解.     

解抛物型方程的分支稳定的高精度显式差分格式

用待定参数法构造了解一维抛物型方程的分支稳定的高精度显式差分格式,截断误差为O（△t^4△x^4),稳定性条件为r=a△t/△x^2＜1/2。     

三维抛物型方程的一个高精度恒稳定的PC格式

对三维抛物型方程,构造了一个高精度恒稳定的PC格式,格式的截断误差阶达到O（△t^2＋△x^4）,通过数值实例验证了所得格式较现有的同类格式的精度提高了二位以上有效数字;然后将Richardson外推法应用于本文格式,得到了具有O（△t^3＋△x^6）阶精度的近似解,并将所得格式推广到了四维情形．     

解三维抛物型方程的一个ADI格式

构造了一个解三维抛物型方程的高精度ADI格式,格式绝对稳定,截断误差为O（△t^2＋△x^4）;然后应用Richerdson外推法,外推一次得到了具有O（△t^3＋△x^6）阶精度的近似解.     

四维抛物型方程的高精度分支稳定的显式差分格式

对四维抛物型方程构造了一个高精度显格式,格式的稳定性条件为r=Δt/Δx2=△t/Δy2=△t/△z2=Δt/Δw2<1/2,截断误差阶达到O(Δt2 Δx4),通过数值实验,表明本文理论分析的正确性和文中格式较同类格式的优越性.     

二维抛物型偏微分方程的绝对稳定显格式

提出了一个解二维抛物型偏微分方程初边值问题的绝对稳定分支三层显式差分格式，格式的局部截断误差阶为Ｏ（△ｔ２＋△ｘ２＋△ｙ２）．实算表明，格式的稳定性能与理论分析是一致的．     

不可压核废料污染问题沿特征线的混合有限元方法

本文对具有分子弥散项的不可压核废料污染问题提出了沿特征方向的混合元离散格式，即对流动方程采用混合元格式，而对浓度方程和传热方程沿特征方向有限元离散。我们的论证表明：该格式具有最优收敛精度；时间步长△ｔ的前置常数仅依赖二阶方向导数；对△ｔ的限制由标准元方法中的△ｔ＝ｏ（ｈ）＾［２］减弱为△ｔ＝Ｏ（ｈ）。     

求解Riesz空间分数阶扩散方程的一种新的数值方法

本文利用Diethelm方法构造了一种逼近Riesz空间分数阶导数的O（△x^3-α）格式,其中1 < α < 2,△x是空间步长.进一步对一阶时间导数采用Crank-Nicolson方法离散,得到了求解Riesz空间分数阶扩散方程的一种新的有限差分格式,并用矩阵方法证明了稳定性和收敛性,其误差估计为O（△t²+△x^3-α）,其中△t为时间步长.最后,数值算例验证了差分格式的正确性和有效性.     

解二维抛物型方程的高精度差分格式

本文构造了一个解二维抛物型方程的高精度三层显式差分格式,其稳定性条件为r=△t/△x2=△t/△y2≤1/4,截断误差为O(△t2+△x4).     

解对流扩散方程的子域精细积分AGEI方法

Based on subdomain precise integration method, a class of two-levelimplicit schemes containing parameter a＞0 for the initial-boundary value prob-lem of convection-diffusion equation are presented. Their local truncation errorsare O(a△t+△t2+△x2). The implicit schemes are unconditionally stable for all a＞0. Then on the basis of the implicit schemes, an alternating group explicit iter-ative (AGEI) method is proposed, and convergence of the iterative process isproved. Because the whole calculation process is explicit, so the AGEI method isvery suitable to parallel arithmetic. Numerical example shows that the AGEImethod has high accuracy and good practicability.     

UNCONDITIONAL STABLE DIFFERENCE METHODS WITH INTRINSIC PARALLELISM FOR SEMILINEAR PARABOLIC SYSTEMS OF DIVERGENCE TYPE

The general finite difference schemes with intrinsic parallelism for the boundary value problem of the semilinear parabolic system of divergence type with bounded measurable coefficients is studied. By the approach of the discrete functional analysis, the existence and uniqueness of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. Moreover the unconditional stability of the general difference schemes with intrinsic parallelism justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete initial data of the original problems in the discrete W_2~(2,1) (Q△) norms. Finally the convergence of the discrete vector solutions of the certain difference schemes with intrinsic parallelism to the unique generalized solution of the original semilinear parabolic problem is proved.     

Convergence Theorems for Non-Self Mappings in CAT(0) Spaces

In this paper, we prove strong convergence of Mann iterative schemes to fixed points of multi-valued demicontractive non-self mappings in complete CAT(0) spaces under appropriate conditions. In addition, △? convergence or strong convergence of Mann iterative scheme to a fixed point of single-valued k-strictly pseudocontractive non-self mapping is obtained. Our theorems improve and unify most of the results in the literature.     

NEW ALTERNATING DIRECTION FINITE ELEMENT SCHEME FOR NONLINEAR PARABOLIC EQUATION

A new alternating direction (AD) finite element (FE) scheme for 3-dimensional nonlinear parabolic equation and parabolic integro-differential equation is studied. By using AD, the 3-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using FE, high accuracy is kept; by using various techniques for priori estimate for differential equations such as inductive hypothesis reasoning, the difficulty arising from the nonlinearity is treated. For both FE and ADFE schemes, the convergence properties are rigorously demonstrated, the optimal H1-and L2-norm space estimates and the 0((△t)2) estimate for time variable are obtained.     

Combined perturbation bounds: Ⅱ. Polar decompositions

In this paper, we study the perturbation bounds for the polar decomposition A= QH where Q is unitary and H is Hermitian. The optimal (asymptotic) bounds obtained in previous works for the unitary factor, the Hermitian factor and singular values of A are σ2r||△Q||2F ≤ ||△A||2F,1/2||△H||2F ≤ ||△A||2F and ||△∑||2F ≤ ||△A||2F, respectively, where ∑ = diag(σ1, σ2,..., σr, 0,..., 0) is the singular value matrix of A and σr denotes the smallest nonzero singular value. Here we present some new combined (asymptotic)perturbation bounds σ2r ||△Q||2F+1/2||△H||2F≤ ||△A||2F and σ2r||△Q||2F+||△∑ ||2F ≤||△A||2F which are optimal for each factor. Some corresponding absolute perturbation bounds are also given.     

关于Poisson群胚的结构

令（ΓP,α,β）是Poisson群胚．如果它的每个α-纤维与β-纤维至多交于一点,则Γ在任一点x的特征分布有直和分解△（x）=△α（x）+△β（x）,其中△α（x）Txα－1（u）,△β（x）Txβ-1（u）且它们都是△（x）的辛子空间．由此得到辛叶Sx的辛子流形S和S,使在映射α之下,S辛微分同胚于P中辛叶Su,在映射β之下,S反辛微分同胚于P中辛叶Sv（定理4和5）．对于一般的Poisson群胚,也可得到类似的S和S,它们差一局部辛微分同胚是唯一确定的（定理6）．把以上结果用于辛群胚,还可得到一些更具体的性质（定理7及其推论）．     

关于三次样条函数导数的某些不等式

设△:。~x。相似文献   

具有跳扩散的美式期权二叉树计算格式的收敛速率

American put option with jump-diffusion can be modelled as a vari- ational inequality problem with an integral term.Under the stability condition (σ~2Δt)/(Δx~2)≤1,whereΔx=ln(S_n 1)/(S_n),the convergence rate O((Δx)~(2/3) (Δt)~(1/3))of the explicit finite scheme for this problem is obtained by using penalization technique. The binomial tree scheme of this model,which is equivalent to the explicit scheme, is convergent by the same rate.