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Optimized decomposition method for solving multi-dimensional Burgers’ equation

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  • Kaushik, Sonali
  • Kumar, Rajesh

Abstract

The objectives of this article are to deal with computing the series solutions of 1D dimensionless Burgers’ equation using the optimized decomposition method (ODM) and the extension of ODM to the system of PDEs which aids in dealing with multi-dimensional Burgers’ equation. Several examples of the inviscid and viscous 1D Burgers’ equations are considered to demonstrate the implementation of the scheme. In this case, it is shown that ODM provides better estimates than the existing Adomian decomposition method (ADM). Owing to the advantage of ODM over ADM, the extension of ODM is used to calculate the semi-analytical approximate solutions of the dimensionless 2D and 3D Burgers’ equations. In most cases, it is observed that the series solution gives the closed-form solution. Moreover, in all the examples, the finite term approximate solutions obtained by the proposed method are shown to provide good accuracy with the exact solutions. The theoretical convergence results are also established to showcase the efficacy of our technique.

Suggested Citation

  • Kaushik, Sonali & Kumar, Rajesh, 2023. "Optimized decomposition method for solving multi-dimensional Burgers’ equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 326-350.
    • Handle: RePEc:eee:matcom:v:208:y:2023:i:c:p:326-350
    DOI: 10.1016/j.matcom.2023.01.043
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    References listed on IDEAS

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    1. Guo, Yan & Shi, Yu-feng & Li, Yi-min, 2016. "A fifth-order finite volume weighted compact scheme for solving one-dimensional Burgers’ equation," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 172-185.
    2. Kedir Aliyi Koroche & Niansheng Tang, 2022. "Numerical Solution of In-Viscid Burger Equation in the Application of Physical Phenomena: The Comparison between Three Numerical Methods," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2022, pages 1-11, March.
    3. Odibat, Zaid, 2020. "An optimized decomposition method for nonlinear ordinary and partial differential equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    4. Zhang, Xu & Jiang, Yanqun & Hu, Yinggang & Chen, Xun, 2022. "High-order implicit weighted compact nonlinear scheme for nonlinear coupled viscous Burgers’ equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 151-165.
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