Analytical and Numerical Study of the Non-linear Burgers’ Equation

Abstract

In this work, we study the nonlinear Burgers’ equation using the Cole- Hopf transformation, which allows converting it into linear parabolic equations. This linearization significantly facilitates the analysis and resolution of the problem. To solve the resulting linear equation, we use the Fourier transform. The solution to the Burgers’ equation is then obtained by combining the solution of the linear equation with the inverse Cole-Hopf transformation. Adiscrete analysis is subsequently performed, complemented by numerical simulations aimed at evaluating the effectiveness of the proposed method.