Research Article Two Computational Strategies for the Approximate Solution of the Nonlinear Gas Dynamic Equations Muhammad Nadeem 1 and Mouad M. H. Ali 2 1 School of Mathematics and Statistics, Qujing Normal University, 655011 Qujing, China 2 Department of Computer Science and Engineering, Hodeidah University, Al-Hudaydah, Yemen Correspondence should be addressed to Mouad M. H. Ali; mouad198080@hoduniv.net.ye Received 14 August 2022; Revised 25 September 2022; Accepted 30 September 2022; Published 13 October 2022 Academic Editor: Arzu Akbulut Copyright © 2022 Muhammad Nadeem and Mouad M. H. Ali. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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. 1. Introduction In recent decades, nonlinear models are particularly describ- ing various physical phenomena in engineering, physics, chemistry, and other sciences. Numerous analytical and numerical schemes have been broadly applied to these non- linear problems. The procedure of obtaining the precise results for the nonlinear problems is very complicated, and it is still a challenging issue to solve these nonlinear PDEs in most of the cases; besides this, there are various strategies for their solution. As a result, various researchers and scien- tists have studied multiple novel methods for getting the analytical solution that are reasonably close to the precise solutions such as the Jacobi elliptic function method [1], Exp ð−Φ ðηÞÞ-expansion method [2], new Kudryashov’s method [3], rank upgrading technique [4], modified expo- nential rational method [5], Hermite-Ritz method [6], resid- ual power series (RPS) method [7], and Adomian decomposition method [8, 9]. He [10, 11] developed an idea of homotopy perturbation method (HPM) to obtain the analytical solution of differen- tial problems. Later, Khuri and Sayfy [12] combined Laplace transform with HPM for the analytical results of differential problems. Nadeem and Li [13] presented a combined approach of Laplace transform with HPM for dealing the analytical work of nonlinear vibration systems and nonlinear wave problems. HPM provides the significant results to solve linear and nonlinear equations of reaction-diffusion equa- tions [14], heat transfer model [15], delay differential equa- tions [16], integro-differential equation [17], and Schrödinger equations [18]. Gas dynamic equations are mathematically modeled by various physical laws such as energy, mass, and momentum conservation. The study of gas motion and its impact on structures using the principles of fluid dynamics and fluid mechanics is known as “gas dynamic,” and it belongs to the discipline of fluid dynamics [19–21]. Jafari [22] pre- sented the idea of variational iteration method (VIM) on the basis of Lagrange multipliers to investigate the analytical solution of nonlinear gas dynamic equation and Stefan equa- tion. Later, Matinfar et al. [23] used a simple procedure using He’s polynomials to obtain the analytical results of GD equation and provided the efficient results to show that the suggested algorithm is quite suitable for such problems. Hindawi Journal of Mathematics Volume 2022, Article ID 8130940, 7 pages https://doi.org/10.1155/2022/8130940