Volume 8, Issue 1
Stability Analysis and Order Improvement for Time Domain Differential Quadrature Method

Adv. Appl. Math. Mech., 8 (2016), pp. 128-144.

Published online: 2018-05

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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.

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fzwang@ctgu.edu.cn (Fangzong Wang)

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@Article{AAMM-8-128, author = {Wang , FangzongLiao , Xiaobing and Xie , Xiong}, title = {Stability Analysis and Order Improvement for Time Domain Differential Quadrature Method}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {1}, pages = {128--144}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2014.m794}, url = {http://global-sci.org/intro/article_detail/aamm/12081.html} }
TY - JOUR T1 - Stability Analysis and Order Improvement for Time Domain Differential Quadrature Method AU - Wang , Fangzong AU - Liao , Xiaobing AU - Xie , Xiong JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 128 EP - 144 PY - 2018 DA - 2018/05 SN - 8 DO - http://doi.org/10.4208/aamm.2014.m794 UR - https://global-sci.org/intro/article_detail/aamm/12081.html KW - AB -

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.

Fangzong Wang, Xiaobing Liao & Xiong Xie. (1970). Stability Analysis and Order Improvement for Time Domain Differential Quadrature Method. Advances in Applied Mathematics and Mechanics. 8 (1). 128-144. doi:10.4208/aamm.2014.m794
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