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Exact Solution of Equation Governing the Unsteady Flow of a Polytropic Gas Using the Natural Decomposition Method

In this article, we introduced a new technique called the Natural Decomposition Method (NDM) for solving the equation governing the unsteady flow of a polytropic gas. The new technique is a combination of the Natural transform Method (NTM) and Adomian Decomposition Method (ADM). The proposed technique is applied directly without using any linearization, discretization, transformation, or taking some restrictive assumptions and it drastically reduce the computational size. Using the new technique, we successfully obtained exact solution of the nonlinear equations governing the unsteady flow of a polytropic gas, and the results are compared with the results of the existing methods. This shows the simplicity, efficiency, reliability and accuracy of the new technique.