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 di erential 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 coe cient 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 modi ed weighting coe cient 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 di erential quadrature analogous equations of the governing di erential equations are established. The other sampling grid points with no associated boundary conditions are not essential