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Mathematical Problems in Engineering
Volume 2015, Article ID 657494, 9 pages
http://dx.doi.org/10.1155/2015/657494
Research Article

Characteristics of the Differential Quadrature Method and Its Improvement

College of Electrical Engineering & New Energy, China Three Gorges University, Yichang, Hubei 443002, China

Received 8 September 2014; Revised 23 December 2014; Accepted 25 December 2014

Academic Editor: Ming-Hung Hsu

Copyright © 2015 Wang Fangzong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The differential quadrature method has been widely used in scientific and engineering computation. However, for the basic characteristics of time domain differential quadrature method, such as numerical stability and calculation accuracy or order, it is still lack of systematic analysis conclusions. In this paper, according to the principle of differential quadrature method, it has been derived and proved that the weighting coefficients matrix of differential quadrature method meets the important -transformation feature. Through the equivalence of the differential quadrature method and the implicit Runge-Kutta method, it has been proved that the differential quadrature method is A-stable and -stage -order method. On this basis, in order to further improve the accuracy of the time domain differential quadrature method, a class of improved differential quadrature method of -stage 2-order have been proposed by using undetermined coefficients method and Padé approximations. The numerical results show that the improved differential quadrature method is more precise than the traditional differential quadrature method.