Analytical and Approximate Solutions of the Nonlinear Gas Dynamic Equation Using a Hybrid Approach

This paper presents the study of a numerical scheme for the analytical solution of nonlinear gas dynamic equation. We use the idea of Laplace-Carson transform and associate it with the homotopy perturbation method (HPM) for obtaining the series solution of the equation. We show that this hybrid approach is excellent in agreement and converges to the exact solution very smoothly. Further, HPM combined with He's polynomial is utilized to minimize the numerical simulations in nonlinear conditions that make it easy for the implementation of Laplace-Carson transform. We also exhibit a few graphical solutions to indicate that this approach is extremely reliable and convenient for linear and nonlinear challenges.

Automated summary

This paper presents a numerical scheme for solving the nonlinear gas dynamic equation. The authors combine the Laplace-Carson transform with the homotopy perturbation method (HPM) to obtain a series solution of the equation. The results show that this hybrid approach is highly accurate and converges smoothly to the exact solution. Additionally, the authors utilize HPM with He's polynomial to minimize numerical simulations in nonlinear conditions, making the implementation of Laplace-Carson transform easier. They also provide graphical solutions to demonstrate the reliability and convenience of this approach for linear and nonlinear challenges.