Generalized Differential Quadrature and Its Application. G.U. Aero Report 9117

Shu, C. and Richards, B. E. (1991) Generalized Differential Quadrature and Its Application. G.U. Aero Report 9117. Technical Report. Department of Aerospace Engineering, University of Glasgow.

Abstract

The technique of differential quadrature (DQ) for the solution of a partial differential equation is extended and generalized in this paper. The general formulation for determining the weighting coefficients of the first order derivative is obtained. A recurrence relationship for determining the weighting coefficients of the second and higher order partial derivatives is also obtained, and it is shown that generalized differential quadrature (GDQ) can be considered as a finite difference scheme of the highest order. Three typical formulas of weighting coefficients for the first order derivative are also given in the paper. The error estimations for the function and derivative approximation, and the eigenvalue structures of some basic GDQ spatial discretization matrices have been studied. The application of GDQ to model problems showed that accurate results can be obtained using a small number of grid points.

• Item Type: Research Reports or Papers (Technical Report)
• Status: Published
• Glasgow Author(s) Enlighten ID: Richards, Prof Bryan
• Authors: Shu, C., and Richards, B. E.
• College/School: College of Science and Engineering > School of Engineering > Autonomous Systems and Connectivity
• Publisher: Department of Aerospace Engineering, University of Glasgow
• Copyright Holders: Copyright © 1991 Department of Aerospace Engineering, University of Glasgow
• Publisher Policy: Reproduced with the permission of the Department