A hybrid approach for the regularized long wave-Burgers equation

Abstract

In this paper, a new hybrid approach based on sixth-order finite difference andseventh-order weighted essentially non-oscillatory finite difference scheme isproposed to capture numerical simulation of the regularized long wave-Burgersequation which represents a balance relation among dissipation, dispersion andnonlinearity. The corresponding approach is implemented to the spatialderivatives and then MacCormack method is used for the resulting system. Sometest problems discussed by different researchers are considered to apply thesuggested method. The produced results are compared with some earlier studies,and to validate the accuracy and efficiency of the method, some error norms arecomputed. The obtained solutions are in good agreement with the literature.Furthermore, the accuracy of the method is higher than some previous workswhen some error norms are taken into consideration.