Regular Perturbation of Inviscid Burger Equation in a Traffic Flow Problem

Abstract

The Inviscid Burger Equation is one of the models which can be applied to one-way traffic flow problem. This model was constructed using transport equation in which the flux density following The Greenshield’s approximation. On its development, distinct flux densities were performed by varying the approximation’s model. This cause changing the velocity value. In this paper, we would like to analyze the perturbation problem in the velocity value for inviscid burger equations using multiple scale method. First, we expanded the solution into polynomial of the perturbation parameter and substitute it into the equation. Next, we obtained new equations based on the identical power of it which are quasilinear and linear equations. The new equations were simply solved using Lagrange-Charpit’s method. Since the exact solution of inviscid burger equation can be found using the characteristic method, therefore we also compared both methods. The results show that both solutions are similar.