带漂移的单侧正规化回火分数阶扩散方程的Crank-Nicolson拟紧格式

基于已有的针对单侧正规化回火分数阶扩散方程的三阶拟紧算法,将该算法的思想应用于带漂移的单侧正规化回火分数阶扩散方程的数值模拟,并结合Crank-Nicolson方法导出数值格式.证明了数值格式的稳定性与收敛性,且数值格式的时间收敛阶和空间收敛阶分别是二阶和三阶.通过数值试验验证了数值格式的有效性和理论结果.     

非光滑时间分数阶齐次扩散方程的修正

当初值不光滑时,时间分数阶齐次扩散方程数值方法的精度会下降.为了得到高阶时间收敛格式,提出加权移位的Grünwald-Letnikov的修正格式,运用Lubich的修正方法,得到非光滑时间分数阶齐次扩散方程的收敛阶仍为O(k²).最后,通过数值算例验证了数值计算结果与理论计算结果一致.     

变系数分数阶对流扩散方程的一种算子矩阵方法

研究带Caputo分数阶导数的变系数对流扩散方程的数值解法.基于Chebyshev cardinal函数,推导Riemann-Liouville分数阶积分的一个有效算子矩阵,以之为基础,提出了变系数分数阶对流扩散方程的一种新的算子矩阵法.该方法将方程的求解转化成矩阵的代数运算,具有计算量小和易于编程等特点.给出数值算例并与一些现有的方法进行比较,结果表明该方法是收敛的且在计算精度上占有优势.     

带非线性源项的Riesz回火分数阶扩散方程的预估校正方法

本文针对带非线性源项的Riesz回火分数阶扩散方程,利用预估校正方法离散时间偏导数,并用修正的二阶Lubich回火差分算子逼近Riesz空间回火的分数阶偏导数,构造出一类新的数值格式.给出了数值格式在一定条件下的稳定性与收敛性分析,且该格式的时间与空间收敛阶均为二阶.数值试验表明数值方法是有效的.     

反应扩散问题的新的绝对稳定hp间断Galerkin方法

针对一类反应扩散问题提出了新的绝对稳定hp间断Galerkin方法,并给出了该方法的误差估计,证明了该方法在L~2范数和H~1范数意义下是最优阶收敛.最后,数值算例验证了理论结果的正确性.     

随机微分方程改进的分裂步单支θ方法的强收敛性

本文提出了一个改进的分裂步单支θ方法,在漂移项系数满足单边Lipschitz条件下,证明了当数值方法的参数θ满足1/2 ≤ θ ≤ 1时,该数值方法对于这类随机微分方程是强收敛的,并在现有文献的基础上将方法的收敛阶从1/2阶提高到1阶;当0 ≤ θ ≤ 1/2时,若漂移项系数进一步满足线性增长条件,该数值方法也是强收敛的,收敛阶为1阶.文末的数值试验验证了理论结果的正确性.     

奇异摄动对流扩散方程组的参数一致的二阶有限差分格式

针对一类奇异摄动对流扩散方程组,在■网格上构造了经典的迎风有限差分格式,并利用闸函数方法证明了数值方法为一阶收敛.在此基础上,设计了一个Richardson外推格式,并严格证明了外推方法的精度为二阶一致收敛.数值实验验证了本文的理论结果.     

非线性随机分数阶延迟积分微分方程Euler-Maruyama方法的强收敛性

本文研究了一类新的模型问题:非线性随机分数阶延迟积分微分方程.当方程中的漂移项和扩散项满足全局Lipschitz条件和线性增长条件时,基于压缩映射原理给出了该方程解存在唯一的充分条件.由于理论求解的困难,构造了一种数值方法(Euler-Maruyama方法),并证得强收敛阶为α-1/2,α∈(1/2,1].最后通过数值试验,验证了这一理论结果.     

变系数双侧空间回火分数阶对流-扩散方程的隐式中点法

针对带非线性源项的变系数双侧空间回火分数阶对流-扩散方程,采用隐式中点法离散一阶时间偏导数,中心差商公式离散对流项,用二阶回火加权移位差分算子逼近左、右Riemann-Liouville空间回火分数阶偏导数,构造了一类新的数值格式.证明了数值方法的稳定性和收敛性,且方法在时间和空间均为二阶收敛.数值试验验证了数值方法的理论分析结果.     

时间分数阶扩散方程的一个新的高阶有限差分/谱逼近

研究时间分数阶扩散方程,结合时间方向的有限差分格式和空间方向的Legendre Collocation谱方法,构造了一个高阶稳定数值格式.数值算例表明该格式是无条件稳定和长时间稳定的,其收敛阶为O(Δt^3-α+N^-m),其中Δt,N和m分别是时间步长,空间多项式阶数以及精确解的正则度.     

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.     

CONTENTS OF VOLUME 30

正~~     

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].     

Laminations minimales résiduellement à 2 bouts

Résumé On décrit toutes les feuilles des laminations minimales dont un ensemble résiduel de feuilles ont 2 bouts.      

Best approximation by downward sets with applications

We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs （W,x）, where ∈ X and W is a closed downward subset of X     

Boundedness of multilinear operators on weighted herz type spaces

In this paper, the author establishes the boundedness of multilinear operators on weighted Herz spaces and Herz-type Hardy spaces. The author also obtains their weak estimates on endpoints. As a special case, the conclusions may lead to the weighted estimates for multilinear Calderon-Zygmund operators.     

THE EXACT CONVERGENCE RATE AT ZERO OF LAGRANGE INTERPOLATION POLYNOMIAL TO |x|α

In this paper we present a generalized quantitative version of a result due to M. Revers concerning the exact convergence rate at zero of Lagrange interpolation polynomial to f(x) = |x|α with on equally spaced nodes in [-1, 1].