Sinc-Legendre collocation method for the non-linear Burgers' fractional equation

Abstract

This paper deals with the numerical solution of the nonlinear
fractional Burgers' equation. The fractional derivatives are
described based on the Caputo sense. We construct the solution
using different approach, that is based on using collocation
techniques. The solution is based on using the Sinc method, which
builds an approximate  solution valid on the entire spatial
domain, and  in the time domain, we use the  shifted Legendre
polynomials to replace the time fractional derivatives. The error
in the approximation  is shown to converge to the exact solution
at an exponential rate. Illustrative examples are given with an
applications from traffic flow,  and the numerical results are
shown to demonstrate the efficiency of the newly proposed method.