A numerical scheme based on weighted average differential quadrature method for the numerical solution of Burgers’ equation

摘要

In this work, a numerical scheme based on weighted average differential quadrature method is proposed to solve time dependent Burgers’ equation with appropriate initial and boundary conditions. In first step, time derivative is discretized by forward difference method. Then, quasilinearization process is used to tackle the non-linearity in the equation. The fully discretization leads to a system of linear equations which is solved by Gauss-elimination method. The method is analyzed for stability and convergence. Finally, the adaptability of proposed scheme is demonstrated by numerical experiments and compared with some existing numerical methods in literature. It is found that the proposed numerical scheme produce accurate results and quite easy to implement.