基于重心插值的二维抛物型方程的局部DQ法  

A Local Differential Quadrature Method Based on Gravity Interpolation for Solving Two-Dimensional Parabolic Differential Equations

作　　者：路小平[1] 赵凤群[1] 蒋卓韵[1] 

机构地区：[1]西安理工大学理学院,陕西西安710054

出　　处：《西安理工大学学报》2013年第3期334-337,共4页Journal of Xi'an University of Technology

基　　金：陕西省教育厅科学研究计划基金资助项目(11JK0524)

摘　　要：针对传统微分求积法的局限性,提出一种基于重心插值的局部微分求积法,并应用于二维微分方程的求解。在该方法中选择重心插值函数作为基函数以保证方法具有很好的数值稳定性。此外,局部微分求积法能够克服微分求积法中节点过多出现的弊病。因而,本研究方法除了具有传统微分求积法计算量少、精度高等优点外,还具有数值稳定性好、节点可以取到很多的优点。以二维Burgers方程组为例,数值结果表明了该算法的有效性。Aiming at the disadvantages of traditional differential quadrature method, a local differential quadrature method based on gravity interpolation is proposed in this paper, and the two-dimensional para- bolic equations are solved by the new method. In this approach, the gravity interpolation function is cho- sen as the basis function, which guarantees that the method has a very good numerical stability. In addi- tion, the local differential quadrature method can overcome the drawback of differential quadrature meth- od when it has too many nodes. Accordingly, the proposed method not only inherits the advantages of the traditional differential quadrature method such as less calculation and high precision, but also owns the merits such as good numerical stability and node-selected flexibility. Two-dimensional Burgers equations are taken as example to explain the application of the method, and the numerical results indicate the ef- fectiveness of this method.

关 键 词：重心插值 局部微分求积法 Burgers方程组 

分 类 号：O241[理学—计算数学]