An algorithm for the Burgers' equation using barycentric collocation method with a high-order exponential Lie-group scheme

Abstract

In order to approximate the solution of the one-dimensional Burgers' equation, an accurate algorithm is developed on the combination of the barycentric collocation technique and a high-order group preserving method for space and time discretization, respectively. We have performed this algorithm on two different test examples for various values of viscosity parameters studied in the literature. The comparisons of the numerical results manifest the improved accuracy of the new algorithm.