The equation modelling the evolution of a foam (a complex porous medium consisting of a set of gas bubbles surrounded by liquid films) is solved numerically. This model is described by the reaction-diffusion differential equation with a free boundary. Two numerical methods, namely the fixed-point and the averaging in time and forward differences in space (the Crank-Nicolson scheme), both in combination with Newton's method, are proposed for solving the governing equations. The solution of Burgers' equation is considered as a special case. We present the Crank-Nicolson scheme combined with Newton's method for the reaction-diffusion differential equation appearing in a foam breaking phenomenon.