Work

Numerical Solution of Burgers’ Equation Using the Explicit andCrank-Nicolson Finite Difference Methods

Year: 2025

Type: article

Abstract: The Burgers’ equation is numerically studied in this paper by using the explicit and Crank-Nicolson finite difference methods. Finite difference approximations are used in place of the derivatives, resulting in a system of equations that, when solved, approximate the solutions to the Burgers’ equation. Additionally, the stability by Von Neumann method and convergence analysis are discussed for both methods. Furthermore, a comparison is done between the exact solutions and the approximate solutions for two test problems. We have shown that there is a high degree of agreement between the approximate and exact solutions. It was also determined that the explicit method exhibits conditional stability, whereas the Crank-Nicolson method remains stable under all conditions.

Source: Eurasian Journal of Science and Engineering

DOI: 10.23918/eajse.v11i3p12

Authors: Younis Sabawi, Mohammed I. Sadeeq, Mardan Ameen

Institutions: Imam Ja’afar Al-Sadiq University, Koya University, Akre University for Applied Sciences

Language: English

Topic: Singular Perturbation, Asymptotics and Difference Schemes

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W7128948834

FWCI:

Cites: 19

Cited by:

Related to: 10