Imposition of boundary conditions by modifying the weighting coefficient matrices in the differential quadrature method

One of the important issues in the implementation of the differential quadrature method is the imposition of the given boundary conditions. There may be multiple boundary conditions involving higher-order derivatives at the boundary points. The boundary conditions can be imposed by modifying the weighting coefficient matrices directly. However, the existing method is not robust and is known to have many limitations. In this paper, a systematic procedure is proposed to construct the modified weighting coefficient matrices to overcome these limitations. The given boundary conditions are imposed exactly. Furthermore, it is found that the numerical results depend only on those sampling grid points where the differential quadrature analogous equations of the governing differential equations are established. The other sampling grid points with no associated boundary conditions are not essential. Copyright © 2002 John Wiley & Sons, Ltd.

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