Application of the generalized differential quadrature rule to eight-order differential equations

Abstract

This work extends the application of the generalized differential quadrature rule (GDQR) to an eighth-order boundary-value differential equation with four boundary conditions at boundaries. The differential quadrature expression and explicit weighting coefficients for the eighth-order differential equation are formulated for a first time to implement the GDQR more accurately. A circular cylindrical single-barrel roof is employed as an example. The numerical results show good accuracy and convergence with only a few sampling points. The application of the GDQR is straightforward and has clear advantages in the implementation of multiple boundary conditions over the existing δ-point technique. The GDQR has demonstrated itself as a general numerical method to solve high-order differential equation with multiple boundary conditions. Copyright © 2001 John Wiley & Sons, Ltd.