Numerical solution of Burger’s equation based on Lax-Friedrichs and Lax-Wendroff schemes

Abstract

This paper represents a classical numerical scheme which enables us to solve non-linear hyperbolic equations numerically. For that purpose, the Lax-Friedrichs and Lax-Wendroff schemes are used to solve the Burger’s equation in order to improve an understanding of the numerical diffusion and oscillations that can be present when using such schemes. By solving the Burger’s equation based on both schemes mentioned, a verification of the numerical features such as accuracy, convergence rate and efficiency of the schemes for given initial and boundary values was made. For both of the schemes simulated, Lax-Wendroff scheme gave more accurate solution for solving a Burger’s equation since it has two degree precision along time compare to the Lax-Friedrichs scheme. However, implementing the Lax-Wendroff scheme needs to solve derivatives up to fourth order, hence need more computational time compare to the Lax-Friedrichs scheme. At the same time, numerical simulation with a different time steps showed a better result of both schemes.