Stability Analysis and Order Improvement for Time Domain Differential Quadrature Method

E-ISSN： 2075-1354|8|1|128-144

ISSN： 2070-0733

Source： Advances in Applied Mathematics and Mechanics, Vol.8, Iss.1, 2015-12, pp. : 128-144

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

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.