Differential Quadrature Method Of The Boundary Problems And Its Applications

The differential quadrature method (DQM) is an attractive numerical method with high efficiency and accuracy. But the conventional DQM is limited in its application to regular regions. To deal with problems on irregular geometric domains, coordinate transformation has to be conducted. The triangular differential quadrature method (TDQM) proposed by Zhong[4, 6], avoid the coordinate transformation. In this paper, the domain decomposition method (DDM) is used for the elliptical boundary problems on a pentagonal region. In every sub-domain, we solve the partial differential equations with TDQ method, namely, triangular differential quadrature domain decomposition (TDQDD) method. With boundary reduction technique, the functional values on internal points can be eliminated. The system of equations which satisfied by the boundary points can be obtained. Numerical results show that is easy and effective for treating the problems on irregular region.Another subject is also researched in this paper. The numerical differentiation is often used when dealing with the differential equations. Using the numerical differentiation, the differential equations can be transformed into algebraic equations. Then we can get the numerical solution from the algebraic equations. But the numerical differentiation process is very sensitive to even a small level of errors. In contrast it is expected that on average the numerical integration process is much less sensitive to errors. In this paper, we provide a new method using the DQ method based on the interpolation of the highest derivative (DQIHD) for the differential equations. The original function is then obtained by integration. In this paper, the DQIHD method was applied to the buckling analysis of thin isotropic plates, the numerical results show that our method is of high accuracy, of good convergence with little computational efforts. And it is easy to deal with the boundary conditions.