The method of lines with different types of space discretization has been used for the study of the behaviour of solutions of two parabolic PDE’s with Brusselator reaction scheme in the form $$ \frac{{\partial x}}{{\partial t}} = \frac{{{D_x}}}{{{L^2}}}\frac{{{\partial ^2}x}}{{\partial {z^2}}} + {x^2}y - (B + 1)x + A $$ (1a) $$ \frac{{\partial y}}{{\partial t}} = \frac{{{D_y}}}{{{L^2}}}\frac{{{\partial ^2}x}}{{\partial {z^2}}} + Bx - {x^2} + y $$ (1b) with boundary conditions of the Dirichlet type x(0,t)=x(1,t)=A y(0,t)=y(1,t)=B/A More details about the model can be found e.g. in[1].