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Stability Analysis and Order Improvement for Time Domain Differential Quadrature Method

Published online by Cambridge University Press:  21 December 2015

Fangzong Wang ,
Xiaobing Liao  and
Xiong Xie
Fangzong Wang*
Affiliation:
College of Electrical Engineering & New Energy, China Three Gorges University, Yichang 443002, China
Xiaobing Liao
Affiliation:
College of Electrical Engineering & New Energy, China Three Gorges University, Yichang 443002, China
Xiong Xie
Affiliation:
College of Electrical Engineering & New Energy, China Three Gorges University, Yichang 443002, China
*
*Corresponding author. Email:fzwang@ctgu.edu.cn (F. Z. Wang)
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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 V-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 s-stage s-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 s-stage 2s-order has been proposed by using undetermined coefficients method and Padé approximations. The numerical results show that the proposed differential quadrature method is more precise than the traditional differential quadrature method.

Keywords

37M0565L0565L0665L20Differential quadrature methodnumerical stabilityorderV-transformationRunge-Kutta methodPadé approximations
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 1 , February 2016 , pp. 128 - 144
Copyright
Copyright © Global-Science Press 2016 

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