L_2逼近高精度格式的基本原理及其应用

１．引言 最近十年来出现各种各样的高精度差分格式用于求解微分方程．其中最重要的是 Ｌｅｌｅ［１］,付德熏［２］和刘秋生［３］等的工作．这些方法的共同点是它们与求解的方程无关．所得的解只在离散点上满足方程．为提高解的分辨率必需增加离散点的数量．正由于第一个特性,这些高精度差分格式在求解各种不同类型的微分方程时并不总是有效的．特别是当解有间断或急剧变化时,求解时达不到预期的精度或出现不合理的振荡．此外,这些方法的另一个重要的缺点是由于边界点上高精度格式难于构造,故在边界点上需要采用较低精度的差分格式,…     

奇异杂交边界点方法求解泊松方程

As a boundary-type meshless method,the singular hybrid boundary node method(SHBNM)is based on the modified variational principle and the moving least square(MLS)approximation,so it has the advantages of both boundary element method(BEM)and meshless method.In this paper,the dual reciprocity method(DRM)is combined with SHBNM to solve Poisson equation in which the solution is divided into particular solution and general solution.The general solution is achieved by means of SHBNM,and the particular solution is approximated by using the radial basis function(RBF).Only randomly distributed nodes on the bounding surface of the domain are required and it doesn't need extra equations to compute internal parameters in the domain.The postprocess is very simple.Numerical examples for the solution of Poisson equation show that high convergence rates and high accuracy with a small node number are achievable.     

Mathematical studies of the solution of Burgers' equations by Adomian decomposition method

In this paper, a novel Adomian decomposition method (ADM) is developed for the solution of Burgers' equation. While high level of this method for differential equations are found in the literature, this work covers most of the necessary details required to apply ADM for partial differential equations. The present ADM has the capability to produce three different types of solutions, namely, explicit exact solution, analytic solution, and semi-analytic solution. In the best cases, when a closed-form solution exists, ADM is able to capture this exact solution, while most of the numerical methods can only provide an approximation solution. The proposed ADM is validated using different test cases dealing with inviscid and viscous Burgers' equations. Satisfactory results are obtained for all test cases, and, particularly, results reported in this paper agree well with those reported by other researchers.     

离散变量结构优化设计的组合算法*

本文首先给出了离散变量优化设计局部最优解的定义,然后提出了一种综合的组合算法.该算法采用分级优化的方法,第一级优化首先采用计算效率很高且经过随机抽样性能实验表明性能较高的启发式算法─—相对差商法,求解离散变量结构优化设计问题近似最优解 X ;第二级采用组合算法,在 X 的离散邻集内建立离散变量结构优化设计问题的(-1,0.1)规划模型,再进一步将其化为(0,1)规划模型,应用定界组合算法或相对差商法求解该(0,1)规划模型,求得局部最优解.解决了采用启发式算法无法判断近似最优解是否为局部最优解这一长期未得到解决的问题,提高了计算精度,同时,由于相对差商法的高效率与高精度,以上综合的组合算法的计算效率也还是较高的.     

Elliptic regularization for the semi-linear telegraph system

The solution of the semi-linear telegraph system is compared with the solution of an elliptic regularization, to which one associates two-point boundary conditions. An asymptotic approximation for the solution of the elliptic regularization is constructed. The method employed here is the boundary function method due to Vishik and Lyusternik. The problem is singularly perturbed of elliptic-hyperbolic type. To conduct this analysis, high regularity with respect to t for the solutions of both problems is required. Finally, the order of this approximation is found in different spaces of functions.     

A hybrid metaheuristic algorithm for dynamic rail car fleet sizing problem

The aim of this paper is to present a model and a solution method for rail freight car fleet sizing problem. The mathematical model is dynamic and multi-periodic and car demands and travel times are assumed deterministic, and the proposed solution method is hybridization of genetic algorithms and simulated annealing algorithms. Experimental analysis is conducted using several test problems. The results of the proposed algorithm and CPLEX software are compared. The results show high efficiency and effectiveness of the proposed algorithm. The solution method is applied to solve fleet sizing problem in the Iran Railways as a case study.     

A cubic spline approximation and application of TAGE iterative method for the solution of two point boundary value problems with forcing function in integral form

In this article, we report an efficient high order numerical method based on cubic spline approximation and application of alternating group explicit method for the solution of two point non-linear boundary value problems, whose forcing functions are in integral form, on a non-uniform mesh. The proposed method is applicable when the internal grid points of solution interval are odd in number. The proposed cubic spline method is also applicable to integro-differential equations having singularities. Computational results are given to demonstrate the utility of the method.     

An analytical approximation for solving nonlinear Blasius equation by NHPM

In this article, an analytic approximation to the solution of Blasius equation is obtained by using a new modification of homotopy perturbation method. The Blasius equation is a nonlinear ordinary differential equation which arises in the boundary layer flow. The comparison with Howart's numerical solution shows that the new homotopy perturbation method is an effective mathematical method with high accuracy. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

A simple perturbation approach to Blasius equation

In this paper, we couple the iteration method with the perturbation method to solve the well-known Blasius equation. The obtained approximate analytic solutions are valid for the whole solution domain. Comparison with Howarth’s numerical solution reveals that the proposed method is of high accuracy, the first iteration step leads to 6.8% accuracy, and the second iteration step yields the 0.73% accuracy of initial slop.