A class of degenerate parabolic equations typically describing the gas flow through porous media is considered. The numerical difficulties in treating such problems arise from the nonlinear degeneracy of the equations. Such problems can be investigated through a parabolic regularization which can be constructed in different ways. On the other hand if positive solutions are sought, the difficulties due to the degeneracy can be overcome by perturbing the data such that the corresponding solutions do admit the value of the degenerate point. The aim of this paper is in using this technique for obtaining the numerical solution, that means to solve numerically the problem with locally perturbed initial and boundary data instead of the prescribed ones. The idea of maximum principle guarantees that the resulting solution takes values away from the degenerate point. This article extends the author's previous results for another class of problems. The efficiency of this method is shown analytically, stability results and error estimates for the numerical to the weak solution are presented. Some numerical experiments at the end of this paper confirm that this new method is comparable with existing ones.