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Two Computational Strategies for the Approximate Solution of the Nonlinear Gas Dynamic Equations

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  • Muhammad Nadeem
  • Mouad M. H. Ali

Abstract

In this article, we propose an idea of Sawi homotopy perturbation transform method (SHPTM) to derive the analytical results of nonlinear gas dynamic (GD) equations. The implementation of this numerical scheme is straightforward and produces the results directly without any assumptions and hypothesis in the recurrence relation. Sawi transform (ST) has an advantage of reducing the computational work and the error of estimated results towards the precise solution. The results obtained with this approach are in the shape of an iteration that converges to the precise solution very gradually. We provide the validity and accuracy of this scheme with the help of illustrated examples and their graphical results. This scheme has shown to be the simplest approach for achieving the analytical results of nonlinear problems in science and engineering.

Suggested Citation

  • Muhammad Nadeem & Mouad M. H. Ali, 2022. "Two Computational Strategies for the Approximate Solution of the Nonlinear Gas Dynamic Equations," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:8130940
    DOI: 10.1155/2022/8130940
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    References listed on IDEAS

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    1. Khaled A. Gepreel & Taher A. Nofal & Ali A. Al-Thobaiti, 2012. "The Modified Rational Jacobi Elliptic Functions Method for Nonlinear Differential Difference Equations," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-30, October.
    2. M. Higazy & Sudhanshu Aggarwal & Taher A. Nofal & Hijaz Ahmad, 2020. "Sawi Decomposition Method for Volterra Integral Equation with Application," Journal of Mathematics, Hindawi, vol. 2020, pages 1-13, December.
    3. Khaled A. Gepreel & Taher A. Nofal & Ali A. Al-Thobaiti, 2012. "The Modified Rational Jacobi Elliptic Functions Method for Nonlinear Differential Difference Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
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