色散方程的一类新的并行交替分段隐格式

本文给出了一组逼近色散方程的非对称差分格式，并用这组格式和对称的Crank-Nicolson型格式构造了求解色散方程的并行交替分段差分隐格式．这个格式是无条件稳定的，能直接在并行计算机上使用．数值试验表明，这个格式有很好的精度．     

一维单个守恒律的一类二阶、几乎熵耗散的格式

本文考虑一维单个守恒律方程，对其设计了一个基于熵耗散的非线性守恒型差分格式．本格式的数值流函数是Lax-Freidrichs格式和Lax-Wendroff格式数值流函数的凸组合，凸组合中的系数是由考虑耗散熵来决定的．这样在解的光滑区域内，格式几乎、甚至完全是Lax-Wendroff格式，而在解的间断处，格式几乎、甚至完全是Lax—Freidrichs格式．从而消除了间断附近的非物理振荡，实现了计算的非线性稳定性．理论分析表明本格式在解的非极值点处是二阶精度的，而在解的极值点处至少有一阶精度．数值试验表明格式是有效的．     

一类时空二阶精度高分辨率MmB差分格式的构造及数值试验

1．引言考虑如下二维双曲型守恒律初值问题的数值解．H．M．Wu和S．L．Yang在文山中给出了MmB差分格式的定义如下：给定（．1）M差分格式定义．若则称格式（1．2）为MmB差分格式．这里BmB表示局部MaximumandminimumBounds．由定义可知，若差分格式（1．2）可写为形式且。＼P’三0，＞。：r’一1．则格式（1．4）为MmB差分格式．j＝l文山构造了二维双曲型守恒律的二类二阶精度的MmB差分格式，使构造二维高分辨格式有了新的突破，但他们是从标量线性双曲型守恒律出发，然后把结果推广到非线性情形．本文直接从二维非线性双曲型守恒律…     

色散方程的一类本性并行的差分格式

对一维色散方程给出了本性并行的一般的交替差分格式，证明了该类格式的绝对稳定性已有的交替分组显格式(AGE)是该类格式的特例．作为特例，进一步得到交替分段显一隐格式(ASF-I)和交替分段Crank-Nicolson格式(ASC-N)．数值实验比较了这几个格式数值解的精确性．     

一类非线性Schrodinger方程的差分／Legendre谱元法

考察一类带幂次非线性项的Schrodinger方程的Dirichlet初边值问题，提出了一个有效的计算格式，其中时间方向上应用了一种守恒的二阶差分隐格式，空间方向上采用Legendre谱元法．对于时间半离散格式，证职了该格式具有能量守恒性质，并给出了L^2误差估计，对于全离散格式，应用不动点原理证明了数值解的存在唯一性，并给出了L^2误差估计．最后，通过数值试验验证了结果的可信性．     

关于U_t=aU_(xx)差分格式的进一步研究(英文)

对于热传导方程构造了两个高阶精度的差分格式，一个是三层七点显格式，另一个是三层九点隐格式．证明了差分格式的收敛性和稳定性，最后给出数值计算结果．     

非线性Schroedinger方程的高精度守恒差分格式

本文首先分析线性Schroedinger方程一种高阶差分格式的构造方法，得到方程的耗散项．在此基础上对三次非线性Schroedinger方程，提出了一种精度为O(r^2 h^2)的差分格式，证明了该格式保持了连续方程的两个守恒量，且是收敛的与稳定的．并通过数值例子与已有隐格式进行了比较，结果表明，本文格式在计算量类似的情况下，提高了数值精度．     

非定常自由面流激波解的二阶守恒算法

将计算双曲型守恒律弱解的Lax-Wendroff型TVD格式推广到断面形状沿程任意变化的一般浅水方程组，构造了二阶精度的差分格式．新格式适用于模拟天然河道中溃坝洪水波的传播．提供了表明方法性能的算例，实际天然梯级水库溃坝问题的数值实验表明格式稳定，适应性强．     

一类带波动算子的非线性Schrodinger方程的一个守恒差分格式

该文对一类带波动算子的非线性Ｓｃｈｒ¨ｏｄｉｎｇｅｒ（ＮＬＳ）方程提出了一个守恒的差分格式，证明了该格式的收敛性和稳定性．数值计算结果表明，该格式对网比不敏感，具有很好的守恒性，并且比文［１］中的不守恒格式提高了计算效率．     

对流扩散方程的新型Crank-Nicholson差分格式

本文针对一维非定常对流扩散方程，构造了一种对角元严格占优的Crank-Nicholson差分格式，利用能量估计的方法对该格式做了稳定性分析．收敛性收分析以及误差估计．数值试验结果表明．该格式具有良好的稳定性．     

A Unified Ternary Curve Subdivision Scheme

A unified $m\,(m>2)$-point ternary scheme with some parameter is proposed. The continuity of subdivision scheme is analyzed based on the relationship between the subdivision scheme and difference scheme. Moreover, the proposed subdivision is extended to asymmetric multi-parameter subdivision and the asymmetric schemes in four cases are presented in detail. Some examples are given to show that the presented scheme has better approximating effect.     

A high-order compact difference scheme for 2D Laplace and Poisson equations in non-uniform grid systems

In this study, a high-order compact scheme for 2D Laplace and Poisson equations under a non-uniform grid setting is developed. Based on the optimal difference method, a nine-point compact difference scheme is generated. Difference coefficients at each grid point and source term are derived. This is accomplished through the consideration of compatibility between the partial differential equation and its difference discretization. Theoretically, the proposed scheme has third- to fourth-order accuracy; its fourth-order accuracy is achieved under uniform grid settings. Two examples are provided to examine performance of the proposed scheme. Compared with the traditional five-point difference scheme, the proposed scheme can produce more accurate results with faster convergence. Another reference scheme with the same nine-point grid stencil is derived based on the five-point scheme. The two nine-point schemes have the same coefficients for each grid points; however, their coefficients for the source term are different. The overall accuracy level of the solution resulting from the proposed scheme is higher than that of the nine-point reference scheme. It is also indicated that the smoothness of grids has significant effects on accuracy and convergence of the solutions; efforts in optimizing the grid configuration and allocation can improve solution accuracy and efficiency. Consequently, with the proposed method, solution under the non-uniform grid setting with appropriate grid allocation would be more accurate than that under the uniform-grid manipulation, with the same number of grid points.     

The parametric synchronization scheme of chaotic system

By constructing the parametric error vectors between drive system and response system, a parametric synchronization scheme of chaotic system which is different from all other schemes is proposed in this paper. Controller of the scheme is designed. The proposed scheme and controller not only realize the synchronization of the state vectors, but also synchronize the unknown response parameters to the given drive parameter as time goes to infinity. That is to say, to achieving the synchronization, we have no need to know the parameters of response system when the parameters of drive system are given. The scheme and controller are successfully applied to the Rössler and the hyperchaotic Rössler systems, corresponding numerical simulations are presented to show the validity of the proposed synchronization scheme and effectiveness of the controller.     

A Newton linearized compact finite difference scheme for one class of Sobolev equations

In this article, a Newton linearized compact finite difference scheme is proposed to numerically solve a class of Sobolev equations. The unique solvability, convergence, and stability of the proposed scheme are proved. It is shown that the proposed method is of order 2 in temporal direction and order 4 in spatial direction. Moreover, compare to the classical extrapolated Crank‐Nicolson method or the second‐order multistep implicit–explicit methods, the proposed scheme is easier to be implemented as it only requires one starting value. Finally, numerical experiments on one and two‐dimensional problems are presented to illustrate our theoretical results.     

Projective synchronization of chaotic fractional-order energy resources demand–supply systems via linear control

A fractional-order energy resources demand–supply system is proposed. A projective synchronization scheme is proposed as an extension on the synchronization scheme of Odibat et al. (2010). The scheme is applied to achieve projective synchronization of the chaotic fractional-order energy resource demand–supply systems. Numerical simulations are performed to verify the effectiveness of the proposed synchronization scheme.     

A scheme for constructing algorithms for correcting a local perturbation in a finite semimetric

A three-step scheme for constructing algorithms for transforming metric information in data mining is proposed and investigated. The correction problem of a local perturbation of a semimetric on a finite set of objects is considered. In the framework of the proposed scheme, algorithms correcting the changes of the distance between a pair of objects by a given quantity that preserve the metric properties are examined. Sufficient conditions under which the correction of semimetrics using the proposed three-step scheme actually completes in two steps and in some special cases even after the first step are obtained. Semimetric similarity functionals are considered, and the correction algorithms are matched to those functionals.     

An efficient heuristic for scheduling in a flowshop to minimize total weighted flowtime of jobs

The problem of scheduling in a flowshop is considered with the objective of minimizing the total weighted flowtime of jobs. A heuristic algorithm is developed by the introduction of lower bounds on the completion times of jobs and the development of heuristic preference relations for the scheduling problem under study. An improvement scheme is incorporated in the heuristic to enhance the quality of its solution. The proposed heuristic, with and without the improvement scheme, and the existing heuristics are evaluated by a large number of randomly generated problems. The results of an extensive computational investigation for various problem sizes are presented. It has been observed that both versions of the proposed heuristic perform better than the existing heuristics in giving a superior solution quality and that the proposed heuristic without the improvement scheme yields a good solution by requiring a negligible CPU time. In addition, an experimental investigation is carried out to evaluate the effectiveness of the improvement scheme when implemented in the proposed heuristic and the existing heuristics, as well as the effectiveness of a variant of the scheme. The results are also discussed.     

用于JPEG2000图像认证的鲁棒性水印算法

针对JPEG2000图像压缩标准所具有的渐进传输、一次编码多次解码等特性,提出了一种基于图像特征的鲁棒性图像认证算法.该算法在JPEG2000编码过程中,先根据图像不变特征,生成认证水印,再根据实际的鲁棒性认证需求,在量化后的小波系数中确定每个子带的认证水印嵌入位平面,最后基于小波系数位平面的特征嵌入认证水印.算法不仅能适应JPEG2000各种灵活的编码方式,还能定位图像篡改的位置.实验结果验证了图像认证算法对可允许图像操作的鲁棒性以及对图像篡改的敏感性.     

求解一维非定常对流扩散反应方程的高精度紧致差分格式

提出了数值求解一维非定常对流扩散反应方程的一种高精度紧致隐式差分格式,其截断误差为O(τ~4+τ~2h~2+h~4),即格式整体具有四阶精度.差分方程在每一时间层上只用到了三个网格节点,所形成的代数方程组为三对角型,可采用追赶法进行求解,最后通过数值算例验证了格式的精确性和可靠性.     

A chaos secure communication scheme based on multiplication modulation

A secure spread spectrum communication scheme using multiplication modulation is proposed. The proposed system multiplies the message by chaotic signal. The scheme does not need to know the initial condition of the chaotic signals and the receiver is based on an extended Kalman filter (EKF). This signal encryption scheme lends itself to cheap implementation and can therefore be used effectively for ensuring security and privacy in commercial consumer electronics products. To illustrate the effectiveness of the proposed scheme, a numerical example based on Genesio-Tesi system and also Chen dynamical system is presented and the results are compared.