A splitting method for the augmented Burgers equation

TL;DR

This paper introduces a splitting method for the augmented Burgers equation, demonstrating its first-order accuracy and analyzing the long-term behavior of solutions, which resemble self-similar solutions of the viscous Burgers equation.

Contribution

The paper presents a novel splitting method for the augmented Burgers equation and provides analysis of its accuracy and asymptotic behavior.

Findings

The splitting method is of first order accuracy.

Solutions exhibit self-similar behavior over large times.

Asymptotic expansion characterizes long-term solution behavior.

Abstract

In this paper we consider a splitting method for the augmented Burgers equation and prove that it is of first order. We also analyze the large-time behavior of the approximated solution by obtaining the first term in the asymptotic expansion. We prove that, when time increases, these solutions behave as the self-similar solutions of the viscous Burgers equation