Polytropic gas systems and their dynamics: analysis using conformable operator

In this paper, the application of the conformable residual power series method (CRPSM) and a new iterative approach, termed the conformable new iterative method (CNIM), in the context of modeling complex systems such as polytropic gas systems is explored. The CRPSM is an effective method to address nonlinear differential equations through using the residuals of the series expansion, and converges even in highly complex and non-linear systems. The CNIM, constructed on the theory of conformable operators, offers an effective alternative to iterative methods, offering higher accuracy and computing performance under the traditional scheme. The paper also examines how conformable operators have been used to characterize behavior of polytropic gas systems that play a significant role in thermodynamic studies. Through these advanced tools of mathematics we will give a justification of their strength in giving good numerical solutions and in the modeling of such systems. Some case studies and numerical experiments to analyze the efficiency of the proposed methods in comparison with classical techniques, their merits in the speed of convergence, stability and precision are described. The findings conclude that the interactions of the CRPSM with the CNIM, more especially by the use of conformable operators, will substantially improve the analysis and simulation of dynamic systems, new directions in solving complex physical and engineering problems.