Approximate solution for unsteady one-dimensional gas flow equation in a porous medium

In this paper, a numerical method is implemented to give approximate solution of an unsteady one-dimensional equation with boundary conditions in infinity. The method is based on the operational matrices of Bernstein polynomials. First, a new problem is obtained using a transmission of interval. Then, an integro-differential equation is derived such that it is equivalent to the transformed differential equation. Finally, a system of algebraic equations is obtained using collocation method and solved by Mathematica software. Illustrative results are included to demonstrate the validity and applicability of the technique.