Distributed Approximating Functional Approach to Burgers’ Equation using Element Differential Quadrature Method

This paper presents a computationally efficient and an accurate methodology in differential quadrature element method (EDQM) analysis of the nonlinear one-dimensional Burgers’ equation. Based on this approach, the total spatial and temporal domain is divided into a set of sub-domain and in each sub-domain, the DQ rule is employed to discretize the spatial and temporal domain derivatives. This equation is similar to, but simpler than, the Navier-Stokes equation in fluid dynamics. To verify this advantage through some comparison studies, an exact series solution are also obtained. In addition, the presented scheme has numerically stable behavior. After demonstrating the convergence and accuracy of the method, the effects of velocity parameters on the viscosity distribution are studied. It is found that element differential quadrature method provides highly accurate an exact series solution for Burgers, equation, while a small number of grid points is needed.