Stability Analysis and Order Improvement for Time Domain Differential Quadrature Method (Advances in Applied Mathematics and Mechanics, 2018)
The differential quadrature method has been widely used in scientific andengineering computation. However, for the basic characteristics of time domain differentialquadrature method, such as numerical stability and calculation accuracy ororder, it is still lack of systematic analysis conclusions. In this paper, according to theprinciple of differential quadrature method, it has been derived and proved that theweighting coefficients matrix of differential quadrature method meets the important\u00a0V-transformation feature. Through the equivalence of the differential quadraturemethod and the implicit Runge-Kutta method, it has been proved that the differentialquadrature method is A-stable and $s$-stage $s$-order method. On this basis, in orderto 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 proposedby using undetermined coefficients method and Pad\u00e9\u00a0approximations. The numerical results show that the proposed differential quadrature method is more precisethan the traditional differential quadrature method.