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 - <p style="text-align: justify;">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&nbsp;<strong>V</strong>-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&nbsp;approximations. The numerical results show that the proposed differential quadrature method is more precise
than the traditional differential quadrature method.</p>