A numerical scheme based on differential quadrature method to solve time dependent Burgers' equation
Purpose - The purpose of this paper is to propose a numerical method to solve time dependent Burgers' equation with appropriate initial and boundary conditions. Design/methodology/approach - The presence of the nonlinearity in the problem leads to severe difficulties in the solution approximation. In construction of the numerical scheme, quasilinearization is used to tackle the nonlinearity of the problem which is followed by semi discretization for spatial direction using differential quadrature method (DQM). Semi discretization of the problem leads to a system of first order initial value problems which are followed by fully discretization using RK4 scheme. The method is analyzed for stability and convergence. Findings - The method is illustrated and compared with existing methods via numerical experiments and it is found that the proposed method gives better accuracy and is quite easy to implement. Originality/value - The new scheme is developed by using some numerical schemes. The scheme is analyzed for stability and convergence. In support of predicted theory some test examples are solved using the presented method.
differential quadrature method burgers' equation quasilinearization runge-kutta method order of convergence differential equations mathematics