This paper presents a comparative study of computational methods for cosmic gas dynamics, focusing on a representative problem in galactic gas dynamics. The authors apply several commonly used algorithms, including the Beam scheme, FCT methods, and a new second-order accurate method, to a one-dimensional model of gas flow in a spiral galaxy. The study highlights the importance of choosing the right algorithm for obtaining reliable results, as some methods, such as the Beam scheme and FCT methods, are found to be unsuitable for the test problem due to their high programming effort and computer time requirements. The methods considered include the Beam scheme, Godunov's method, second-order flux-splitting method (FS2), MacCormack's method (MC2), and Flux-Corrected Transport (FCT) methods. The Beam scheme, while widely used in astrophysics, is found to have strong numerical diffusion, leading to an underestimation of the density maximum and displacement of the shock downstream. Godunov's method, though more accurate, still shows some numerical diffusion. The second-order methods, FS2 and MC2, perform significantly better, with FS2 being the most accurate and efficient, requiring less than twice the computation time of the first-order methods. The study concludes that the second-order upwind-differencing method FS2 is recommended for solving flow problems involving shocks, while MC2 is suitable for smoother problems. The results also suggest that monotonicity algorithms for second-order methods are effective and that the choice of method should consider the specific characteristics of the problem, such as the presence of shocks and the need for accuracy in smooth regions.This paper presents a comparative study of computational methods for cosmic gas dynamics, focusing on a representative problem in galactic gas dynamics. The authors apply several commonly used algorithms, including the Beam scheme, FCT methods, and a new second-order accurate method, to a one-dimensional model of gas flow in a spiral galaxy. The study highlights the importance of choosing the right algorithm for obtaining reliable results, as some methods, such as the Beam scheme and FCT methods, are found to be unsuitable for the test problem due to their high programming effort and computer time requirements. The methods considered include the Beam scheme, Godunov's method, second-order flux-splitting method (FS2), MacCormack's method (MC2), and Flux-Corrected Transport (FCT) methods. The Beam scheme, while widely used in astrophysics, is found to have strong numerical diffusion, leading to an underestimation of the density maximum and displacement of the shock downstream. Godunov's method, though more accurate, still shows some numerical diffusion. The second-order methods, FS2 and MC2, perform significantly better, with FS2 being the most accurate and efficient, requiring less than twice the computation time of the first-order methods. The study concludes that the second-order upwind-differencing method FS2 is recommended for solving flow problems involving shocks, while MC2 is suitable for smoother problems. The results also suggest that monotonicity algorithms for second-order methods are effective and that the choice of method should consider the specific characteristics of the problem, such as the presence of shocks and the need for accuracy in smooth regions.