Differential Quadrature Methods and its Applications

In the past few years, the differential quadrature (DQ) method has been extensively applied in engineering. This book gives a systematic description of the mathematical fundamentals for the DQ method and its detailed implementation in solving the flow, structural, as well as Helmholtz problems. The DQ method is a global approach for numerical discretization, which approximates the derivatives by a linear wighted sum of all the functional values in the whole domain. Following the analysis of function approximation and the analysis of a linear vector space, it is shown in the book that the weighting coefficients of the polynomial-based, Fourier expansion-based, and the exponential-based DQ methods can be computed explicitly. It is also demonstrated that the polynomial-based DQ method is equivalent to the highest order finite difference scheme. Furthermore, the relationship between the DQ method and the conventional spectral collocation method is analyzed. Three FORTRAN programs are attached respectively for simulation of driven cavity flow, vibration analysis of plate, and Helmholtz eigenvalue problem. It is believed that through the three sample programs, the readers can understand the DQ method better and can easily modify the programs to solve their own engineering problems.