Abstract
In Part 1 of this paper, the sampling grid points for the differential quadrature method to give unconditionally stable higher-order accurate time step integration algorithms are proposed to solve first-order initial value problems. In this paper, the differential quadrature method is extended to solve second-order initial value problems. The conventional approaches to impose the given initial conditions are discussed. A new approach to impose the given initial conditions is then presented. It is found that the proposed approach could generate unconditionally stable higher-order accurate time step integration algorithms for second-order equations directly. Furthermore, the procedure can be generalized to construct unconditionally stable higher-order accurate time step integration algorithms for third- and higher-order initial value problems without any difficulties. The computational procedures for multi-degree-of-freedom systems and non-linear problems are also discussed. As demonstrated by the numerical examples, the differential quadrature method using the proposed sampling grid points and the proposed method to impose the given initial conditions is found to be more efficient than the conventional differential quadrature method in solving initial value problems. Copyright © 2001 John Wiley & Sons, Ltd.
Published Version
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