Generalized differential quadrature rule for initial-value differential equations

Abstract

The generalized differential quadrature rule (GDQR) proposed recently by the authors is applied here to solve initial-value differential equations of the 2nd to 4th order. Differential quadrature expressions are derived based on the GDQR for these equations. The Hermite interpolation functions are used as trial functions to obtain the explicit weighting coefficients for an easy and efficient implementation of the GDQR. The numerical solutions for example problems demonstrate that the GDQR has high efficiency and accuracy. A detailed discussion on the present method is presented by comparing with other existing methods. The present method can be extended to other types of differential equation systems.