Numerical study of the space fractional Burger’s equation by using Lax-Friedrichs-implicit scheme

Abstract

This paper deals with the numerical solution of space fractional Burger’s equation using the implicit finite difference scheme and Lax-Friedrichs implicit finite difference scheme respectively. The Riemann-Liouville based fractional derivative (non-integer order) is fitted for the diffusion term of fractional order 1.0 < α ≤ 2.0. The Mathematical induction is used to estimate a stability of both the implicit and Lax-Friedrichs-implicit schemes. The study shows that the implicit based scheme is stable and the results are good in agreement with the exact solution. Finally, the significance of space fractional order with respect to the solution is discussed. It is noted that the solution of space fractional Burger’s equation get affected by changing the space fractional order.