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

This work extends the application of the generalized differential quadratur e rule (GDQR) to an eighth-order boundary-value differential equation with four boundary conditions at boundaries. The differential quadrature express ion and explicit weighting coefficients for the eighth-order differential e quation are formulated for a first time to implement the GDQR more accurate ly. A circular cylindrical single-barrel roof is employed as an example. Th e numerical results show good accuracy and convergence with only a few samp ling points. The application of the GDQR is straightforward and has clear a dvantages in the implementation of multiple boundary conditions over the ex isting delta -point technique. The GDQR has demonstrated itself as a genera l numerical method to solve high-order differential equation with multiple boundary conditions. Copyright (C) 2001 John Wiley & Sons, Ltd.