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

Authors

  • Younis Sabawi Department of Mathematics, Faculty of Science and Health, Koya University, Koya 44023, Kurdistan Region - F.R. Iraq, College of Information Technology, Imam Ja’afar AL-Sadiq University, Baghdad, Iraq. https://orcid.org/0000-0002-9807-8409
  • Mohammed I. Sadeeq Department of Mathematics, College of Education, Akre University for Applied Sciences, Akre, Kurdistan Region, Iraq. https://orcid.org/0009-0006-9278-6953
  • Mardan Ameen Department of Mathematics, Faculty of Science and Health, Koya University, Koya 44023, Kurdistan Region - F.R. Iraq https://orcid.org/0000-0002-3234-1825

DOI:

https://doi.org/10.23918/eajse.v11i3p12

Keywords:

Burgers’ equation, Finite difference method, Explicit method, Crank-Nicolson method, Von Neumann stability, Convergence analysis

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.

Author Biography

  • Mardan Ameen, Department of Mathematics, Faculty of Science and Health, Koya University, Koya 44023, Kurdistan Region - F.R. Iraq

    Numerical Analysis

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Published

2026-02-03

Issue

Vol. 11 No. 3 (2025)

Section

Articles

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Copyright (c) 2026 Younis Sabawi, Mohammed I. Sadeeq, Mardan Ameen

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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Eurasian J. Sci. Eng is distributed under the terms of the Creative Commons Attribution License 4.0 (CC BY-4.0) https://creativecommons.org/licenses/by/4.0/

How to Cite

Sabawi, Y., I. Sadeeq, M. ., & Ameen, M. (2026). Numerical Solution of Burgers’ Equation Using the Explicit andCrank-Nicolson Finite Difference Methods. EURASIAN JOURNAL OF SCIENCE AND ENGINEERING, 11(3), 199-214. https://doi.org/10.23918/eajse.v11i3p12

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