Numerical and Analytical Solution of Gas Flow Through a Micro-Nano Porous Media: A Comparison

In this paper, we study a non-linear two-point boundary value problem (BVP) on semi-infinite interval that describes the unsteady gas equation. The solution of the mentioned ordinary differential equation (ODE) is investigated by means of the Hermite functions collocation method and the Homotopy analysis method (HAM). The Hermite functions collocation method reduces the solution of above-mentioned problem to the solution of a system of algebraic equations and finds its the numerical solution. The homotopy analysis method is also one of the most effective methods in obtaining series solutions for these types of problems and finds their analytic solution. Through the convergence of these methods we determine the accurate initial slope y′(0) with good capturing the essential behavior of y(x). Numerical and analytical evaluations and comparisons with the results obtained are also discussed at the last part of the paper.