# Numerical Simulation of Burgers’ Equation

## Abstract

An exponential finite difference technique is first presented by Bhattacharya for one‐

dimensional unsteady state. In this study, the exponential finite difference technique was

used to solve the Burgers’ equation in one‐dimensional with different value of h (step

size). Burgers’ equation is considered in this study because the equation governing simple

nonlinear diffusion process. Since the Burgers’ equation is nonlinear, the Hopf‐Cole

transformation is applied to the linear heat equation which was converted from Burgers’

equation. Then, the exponential finite difference methods are used to obtain numerical

solution. Three techniques have been implemented namely explicit exponential finite

difference method, implicit exponential finite difference method and modified Burgers’

equation using explicit exponential finite difference method. In the solution process, the

explicit exponential finite difference method used a direct to solve the Burgers’ equation

while the implicit exponential finite difference method leads to a system of nonlinear

equation. At each time‐level, Newton’s method is used to solve the nonlinear system. The

solution of the one‐dimensional modified Burgers’ equation is using the explicit

exponential finite difference method. The solution process has discretized the time

derivative and spatial derivative using exponential finite difference technique. Numerical

solutions for each method are compared with exact solution and the results obtained

using the three methods are precise and reliable. The percent errors are computed and

found to be sufficiently small.

## Keywords:

Burgers’ equation, explicit exponential finite difference method, implicit exponential finite difference method, modified Burgers’ equation## Downloads

## Published

## How to Cite

*Applied Mathematics and Computational Intelligence (AMCI)*,

*6*, 73–82. Retrieved from https://ejournal.unimap.edu.my/index.php/amci/article/view/188