Differential quadrature method based on the highest derivative and its applications

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 and Winkler plates, the numerical results agree well with the analytic solutions, and the 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.