An Improved Differential Quadrature Time Element Method

Abstract

A Differential Quadrature Time Element Method (DQTEM) was proposed by the author and co-worker, its drawback is the need of larger storage capacity since the dimension of the coefficients matrix for solution is the product of both spatial degrees of freedom and temporal degrees of freedom. To solve this problem, an improved DQTEM is developed in this work, in which the differential quadrature method is used to discretize both spatial and time domains, sequentially, and the dimension of the coefficients matrix is greatly reduced without losing solution accuracy. Theoretical studies demonstrate the improved DQTEM features superiorities including higher-order accuracy, adequate stability and symplectic characteristics. The improvement of DQTEM is validated by extensive comparisons of the present DQTEM with the original DQTEM.

Keywords

• differential quadrature rule
• direct integration method
• time element
• symplectic