Numerical solution of burgers’ equation using fourier expansion based on differential quadrature method

Abstract

The Fourier expansion-based differential quadrature (FDQ) method was applied in this work to solve one-dimensional Burgers’ equation with appropriate initial and boundary conditions. In the first step for the given problem we have discretized the interval and replaced the differential equation by the Fourier expansion basis based on differential quadrature (FDQ) to obtain a system of ordinary differential equation (ODE). The obtained ordinary differential equation was solved by fourth order classical Range-Kutta method. Finally the validation of the present scheme was demonstrated by numerical example and compared with some existing numerical methods in literature. The method is analyzed for stability and convergence. It is found that the proposed numerical scheme produce accurate results and quite easy to implement.