A Mathematical Approach to the New Homotopy-Permeation Method for Solving the Gas Dynamics Equation

Abstract

In this paper, we introduce a new homogeneous Perturbation method (NHPM) to find analytical solutions to linear and non-linear gas dynamics equations. Using NHPM, it is possible to obtain a quasi-analytical solution, revealing the key points of the problem or the closed-form approximate solution to the problem.The calculation of examples shows simplicity and less manipulation than the other methods. The 3-dimension graphical representations of linear and non-linear GD equations are also provided to validate that mathematical approach. Here we use MATLAB to generate systematic results and graphical representations.