Numerical Solution of Partial Differential Equations using Differential Quadrature Methods

Abstract

Solving the partial differential equation (PDE) using the differential quadrature (DQ) method is receiving special interest as it requires less memory and computational time. The method uses fewer number of grid points for results with an acceptable error. The method also has advantages over other techniques in case of formulating non-uniform grids. Different differential quadrature methods are presented and some of them are applied to solve the two dimensional Poisson equation. Advantages of each technique over the previous techniques are presented. Examples of two dimensional Poisson equation under Dirichlet and mixed boundary conditions are studied using the methods. Comparisons between the results of using the methods to solve the two dimensional Poisson equation are presented