Abstract
In the present paper, we have applied the optimal auxiliary function method (OAFM) for obtaining an analytical solution for solving unsteady flow of gas through a porous medium, which is strongly nonlinear boundary value problem on semi-infinite domain. Our technique finds the solution without any perturbation, discretization, linearization or restrictive assumption as it is like the existence of small or large parameters. This procedure reduces the solutions of this nonlinear problem to the solutions of two linear differential equations, avoiding the complexity provided by other known techniques. Finally, by comparing the results obtained through OAFM with some other procedures, it shows that our technique is effective, highly efficient and controls the convergence approximate solutions using a very fast convergence after only one iteration. Also, numerical values are performed in order to validate the analytical results. The results obtained in this paper are very good in comparison with the numerical results and those known in the literature.
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