解四阶抛物型方程高精度紧致差分格式

针对四阶抛物型方程周期初值问题,提出了一个两层隐式差分格式和一个三层隐式差分格式.它们的局部截断误差分别为O((Δt)2+(Δx)4)和O((Δt)2+(Δt)(Δx)2+(Δx)4),其中Δt,Δx分别为时间步长和空间步长.误差分析和数值实验均表明,本文构造的差分格式比经典的Crank-Nicolson格式和Saul’ev构造的差分格式精度更高.从精度及稳定性方面考虑,本文构造的格式也比文[5]的显式格式要好.     

解三维抛物型方程的一个新的高精度显格式

本文构造了一个解三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=Δt/Δx2=Δt/Δy2=Δt/Δz2≤1/4,截断误差为O(Δt2+Δx4).     

解抛物型方程的一族高精度差分格式

1 引言 求解抛物型方程 u/t=u/x~2, 00, (1) 初边值问题的差分格式,精度高者当属[1]、[2]中的格式.本文对上述问题构造了一族三层(特殊情况下是两层)双参数、绝对稳定、高精度三对角线型的隐式格式,它不仅包含了[1]、[2]中所有的格式,而且还可以得到一个截断误差为O(Δt~3+Δx~4)的绝对稳定的差分格式,精度比[1]、[2]中的格式都高. 2 差分格式 设Δt为时间步长,Δx=L/M(M为正整数)为空间步长,网函数u(jΔx,nΔt )记为u_j~n,对     

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).     

三维热传导方程的一族两层显式格式

提出了一族三维热传导方程的两层显式差分格式,当截断误差阶为O(Δt+(Δx)2)时,稳定性条件为网格比r=Δt/(Δx)2=Δt/(Δy)2=Δt/(Δz)2≤1/2,优于其他显式差分格式。而当截断误差阶为O((Δt)2+(Δx)4)时,稳定性条件为r≤1/6,包含了已有的结果。     

二维抛物型方程的一族高精度显式差分格式

构造了一族解二维抛物型方程的高精度显格式 ,其稳定性条件为r=Δt/Δx2 =Δt/Δy2 <1 /2 ,截断误差为O(Δt3 +Δx4)     

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.     

高阶Schrdinger方程双参数高精度恒稳差分格式

对高阶Schr dinger方程 u t=i( - 1 ) m 2mu x2m 构造一族含双参数的三层高精度隐式差分格式 .当参数α=1 /2 ,β =0时得到一个两层格式 .并证明了 :对任意非负参数α≥ 0 ,β≥ 0该格式都是绝对稳定的 ,并且其截断误差阶达到O( (Δt) 2 (Δx) 6) .数值例子表明 :本文所建立的差分格式是有效的 ,理论分析与实际计算相吻合     

抛物型方程的一个新的高精度恒稳定的隐式差分格式

本文用待定参数法对一维抛物型方程构造出一个截断误差为 0 (△ t3+△ x6)的隐式差分格式 ,格式绝对稳定且可用追赶法求解 .     

一类演化方程的一族双参数恒稳差分格式

对一类演化方程δu/δt=aδ^2m 1u/δx^2m 1(a为常数，m为正整数）构造一族含双参数的三层高精度隐式差分格式。当参数α=1/2,β=0时得到一个双层格式。并证明了：该格式对任意非负参数α≥0，β≥0都是绝对稳定的，并且其截断误差阶为0（（Δt)^2 (Δx)^4).数值例子表明：本文所建立的差分格式是有效的，理论分析与实际计算相吻合。     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].