一类新的求解双边障碍问题的数值方法

针对双边障碍问题的离散互补形式,提出了一类新的格式将其等价转化为方程组的形式,并采用牛顿迭代法进行求解.实验结果显示所提算法能快速,有效地计算出数值解和接触集.     

离散分红下障碍期权的间接级数展开定价方法

人们投资股票市场的最大动力,除了从股票本身的升值中获利,还包括收益分红.提出了带有离散分红的障碍期权的一种新型的近似方法,以向上敲出看涨障碍期权为例,固定分红的次数,通过泰勒级数展开得到关于关键变量的仿射函数,给出了一个只带有一维积分的定价公式,提高了计算速度.该方法还可以用于回望期权等其它衍生品的定价,对在市场上进行期权交易有一定指导意义.     

离散系统分析和参数估计的DPOFS方法

本文借助于DPOFS(离散正交脉冲函数)对离散线性系统和离散双线性系统的分析和参数估计提出了新的方法,这种方法利用:DPOFS的运算矩阵把差分方程转变为代数方程,并由于DPOFS比离散Walsh级数等离散级数在计算方面更加方便和直观,从而使计算大大简化,本文给出了具体实例,分析结果说明了此法的有效性。     

跳跃扩散下双障碍期权定价的数值解

提出了一种求解带有跳跃的双障碍期权定价模型的数值方法.算法采用了Crank-Nicolson 有限差分格式和复化梯形公式对模型进行离散,对离散后的线性系统采用GMRES迭代法求解,并且构造了一个新的预处理算子以加速迭代法的收敛.数值实验验证了该方法能快速求解模型并达到二阶收敛精度.     

同位网格界面速度插值方法研究

讨论了同位网格下,离散的连续性方程、动量方程及标量方程中控制容积界面上速度的计算方法．分别采用动量插值技术和线性插值技术计算了动量方程和标量方程的离散系数中的界面速度,并将两种方法得到的计算结果进行了比较．指出当采用线性插值技术去计算离散方程系数中的界面速度时,离散系数中的质量残余必须等于0,这样才能保证数值解的准确性和计算的收敛速度．     

非饱和土壤水流问题的CN有限元格式

首先给出二维非饱和土壤水流问题基于Crank-Nicolson(CN)方法的具有时间二阶精度的半离散化格式,然后直接从CN时间半离散化格式出发,建立具有时间二阶精度的全离散化CN有限元格式,并给出误差估计,最后用数值例子说明全离散化CN有限元格式的优越性.这种方法可以绕开关于空间变量的半离散化格式的讨论,提高时间离散的精度,极大地减少时间方向的迭代步,从而减少实际计算中截断误差的积累,提高计算精度和计算效率.     

二维土壤溶质输运问题的CN有限元法

首先给出二维土壤溶质输运问题时间二阶精度的Crank-Nicolson(CN)时间半离散化格式,然后直接从CN时间半离散化格式出发,建立具有时间二阶精度的全离散化CN有限元格式,并给出CN有限元解的误差分析,最后用数值例子验证全离散化CN有限元格式的优越性.这种方法提高了时间离散的精度,并极大地减少时间方向的迭代步,从而减少实际计算中截断误差的积累,提高计算精度和计算效率.而且方法绕开对空间变量半离散化有限元格式的讨论,使得理论研究更简便.     

非饱和土壤水流方程的CN广义差分法

首先给出二维非饱和土壤水流方程时间二阶精度的Crank-Nicolson(CN)时间半离散化格式,然后直接从CN时间半离散化格式出发,建立具有时间二阶精度的全离散化CN广义差分格式,并给出误差分析,最后用数值例子验证全离散化CN广义差分格式的优越性.这种方法能提高时间离散的精度,极大地减少时间方向的迭代步,从而减少实际计算中截断误差的积累,提高计算精度和计算效率.而且该方法可以绕开对空间变量的半离散化广义差分格式的讨论,使得理论研究更简便.     

一类椭圆型变分不等式离散问题的迭代算法

根据一类椭圆型变分不等式离散问题所具有的非线性特征，提出了一种简明快速的迭代算法，该方法在解决障碍问题及流体润滑油膜破裂自然边值问题等工程应用问题时具有较高的效率。     

对流扩散方程的缩减基有限元法的后验误差

将缩减基(RB)方法和有限元方法相结合,在保证偏微分方程的有限元离散格式具有足够高精确度前提下,能够大幅度地降低有限元离散格式的维数,从而大大降低计算中内存容量和计算时间的消耗.针对对流扩散方程建立基于RB方法的Crank-Nicolson有限元离散格式,并给出后验误差估计结果.     

Instructions for Authors

<正>Submission Authors must use LaTeX for typewriting,and visit our website www.actamath.com to submit your paper.Our address is Editorial Office of Acta Mathematica Sinica,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

正August 10-14,2015Beijin,China The International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

FRACTIONAL INTEGRALS OF THE WEIERSTRASS FUNCTIONS： THE EXACT BOX DIMENSION

The present paper investigates the fractal structure of fractional integrals of Weierstrass functions. The ezact box dimension for such functions many important cases is established. We need to point out that, although the result itself achieved in the present paper is interesting, the new technique and method should be emphasized. These novel ideas might be useful to establish the box dimension or Hausdorff dimension (especially for the lower bounds) for more general groups of functions.     

English Series

正1 Aims and Scope Acta Mathematicae Applicatae Sinica(English Series)is a quarterly journal established by the Chinese Mathematical Society.The journal publishes high quality research papers from all branches of applied mathematics,particularly welcomes those from partial differential equations,computational mathematics,applied probability,mathematical finance,statistics,dynamical systems,optimization and management science.     

CHINESE ANNALS OF MATHEMATICS SERIES B Volume 35 · 2014 TOTAL CONTENTS

<正>~~     

Congruences,ideals and annihilators in standard QBCC-algebras

We characterize congruence lattices of standard QBCC-algebras and their connection with the congruence lattices of congruence kernels. Work on the paper was supported by Council of Czech Government No J14/98:153100011.     

A decomposition of continuity via ideals

A new class of sets in ideal topological spaces is introduced and using these sets, a decomposition of continuity is given.      

When a compact (countably compact) set is closed. II

We obtain (a) necessary and sufficient conditions and (b) sufficient conditions for a compact (countably compact) set to be closed in products (sequential products) and subspaces (sequential subspaces) of normal spaces. As a consequence of these, sufficient conditions are obtained for (i) the closedness of arbitrary (countable) union of closed sets and (ii) the equality of the union of the closures and the closure of the union of arbitrary (countable) families of sets in these spaces. It is also shown that these results do not hold for quotients of even T ₄,-spaces.     

ASYMPTOTIC BEHAVIOR OF ECKHOFF＇S METHOD FOR FOURIER SERIES CONVERGENCE ACCELERATION

The current paper considers the problem of recovering a function using a limited number of its Fourier coefficients. Specifically, a method based on Bernoulli-like polynomials suggested and developed by Krylov, Lanczos, Gottlieb and Eckhoff is examined. Asymptotic behavior of approximate calculation of the so-called ＂jumps＂ is studied and asymptotic L2 constants of the rate of convergence of the method are computed.