The generalized differential quadrature rule for fourth-order differential equations

The generalized di erential quadrature rule (GDQR) proposed here is aimed at solving high-order di erential equations. The improved approach is completely exempted from the use of the existing -point technique by applying multiple conditions in a rigorous manner. The GDQR is used here to static and dynamic analyses of Bernoulli{Euler beams and classical rectangular plates. Numerical error analysis caused by the method itself is carried out in the beam analysis. Independent variables for the plate are rst de ned. The explicit weighting coe cients are derived for a fourth-order di erential equation with two conditions at two di erent points. It is quite evident that the GDQR expressions and weighting coe cients for two-dimensional problems are not a direct application of those for one-dimensional problems. The GDQR are implemented through a number of examples. Good results are obtained in this work