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[Retracted] A Comparison of Finite Difference and Finite Volume Methods with Numerical Simulations: Burgers Equation Model

Author

Listed:
  • Ali Hasan Ali
  • Ahmed Shawki Jaber
  • Mustafa T. Yaseen
  • Mohammed Rasheed
  • Omer Bazighifan
  • Taher A. Nofal

Abstract

In this paper, we present an intensive investigation of the finite volume method (FVM) compared to the finite difference methods (FDMs). In order to show the main difference in the way of approaching the solution, we take the Burgers equation and the Buckley–Leverett equation as examples to simulate the previously mentioned methods. On the one hand, we simulate the results of the finite difference methods using the schemes of Lax–Friedrichs and Lax–Wendroff. On the other hand, we apply Godunov’s scheme to simulate the results of the finite volume method. Moreover, we show how starting with a variational formulation of the problem, the finite element technique provides piecewise formulations of functions defined by a collection of grid data points, while the finite difference technique begins with a differential formulation of the problem and continues to discretize the derivatives. Finally, some graphical and numerical comparisons are provided to illustrate and corroborate the differences between these two main methods.

Suggested Citation

  • Ali Hasan Ali & Ahmed Shawki Jaber & Mustafa T. Yaseen & Mohammed Rasheed & Omer Bazighifan & Taher A. Nofal, 2022. "[Retracted] A Comparison of Finite Difference and Finite Volume Methods with Numerical Simulations: Burgers Equation Model," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:9367638
    DOI: 10.1155/2022/9367638
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    1. Barakah Almarri & Ali Hasan Ali & António M. Lopes & Omar Bazighifan, 2022. "Nonlinear Differential Equations with Distributed Delay: Some New Oscillatory Solutions," Mathematics, MDPI, vol. 10(6), pages 1-10, March.
    2. H. Thameem Basha & Karthikeyan Rajagopal & N. Ameer Ahammad & S. Sathish & Sreedhara Rao Gunakala & Mustafa Cagri Kutlu, 2022. "Finite Difference Computation of Au-Cu/Magneto-Bio-Hybrid Nanofluid Flow in an Inclined Uneven Stenosis Artery," Complexity, Hindawi, vol. 2022, pages 1-18, April.
    3. Wubshet Ibrahim & Gosa Gadisa, 2019. "Finite Element Method Solution of Boundary Layer Flow of Powell-Eyring Nanofluid over a Nonlinear Stretching Surface," Journal of Applied Mathematics, Hindawi, vol. 2019, pages 1-16, July.
    4. H. Thameem Basha & Karthikeyan Rajagopal & N. Ameer Ahammad & S. Sathish & Sreedhara Rao Gunakala, 2022. "Finite Difference Computation of Au‐Cu/Magneto‐Bio‐Hybrid Nanofluid Flow in an Inclined Uneven Stenosis Artery," Complexity, John Wiley & Sons, vol. 2022(1).
    5. Wubshet Ibrahim & Gosa Gadisa, 2019. "Finite Element Method Solution of Boundary Layer Flow of Powell‐Eyring Nanofluid over a Nonlinear Stretching Surface," Journal of Applied Mathematics, John Wiley & Sons, vol. 2019(1).
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