Author Description

In the past few years, the differential quadrature method has been applied extensively in engineering. This book, aimed primarily at practising engineers, scientists and graduate students, gives a systematic description of the mathematical fundamentals of differential quadrature and its detailed implementation in solving Helmholtz problems and problems of flow, structure and vibration. Differential quadrature provides a global approach to numerical discretization, which approximates the derivatives by a linear weighted 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 exponential-based differential quadrature methods can be computed explicitly. It is also demonstrated that the polynomial-based differential quadrature method is equivalent to the highest-order finite difference scheme. Furthermore, the relationship between differential quadrature and conventional spectral collocation is analysed.<br>The book contains material on:<br>- Linear Vector Space Analysis and the Approximation of a Function;<br>- Polynomial-, Fourier Expansion- and Exponential-based Differential Quadrature;<br>- Differential Quadrature Weighting Coefficient Matrices;<br>- Solution of Differential Quadrature-resultant Equations;<br>- The Solution of Incompressible Navier-Stokes and Helmholtz Equations;<br>- Structural and Vibrational Analysis Applications;<br>- Generalized Integral Quadrature and its Application in the Solution of Boundary Layer Equations.<br>Three FORTRAN programs for simulation of driven cavity flow, vibration analysis of plate and Helmholtz eigenvalue problems respectively, are appended. These sample programs should give the reader a better understanding of differential quadrature and can easily be modified to solve the readers own engineering problems.<br>