Approximate solutions of the initial value problem for reaction diffusion equations in two regions (cells) are obtained. The system is considered here with two chemical species, species $A$ and the autocatalyst $B$. The reaction is taken to be cubic in the autocatalysis in the first region with linear exchange through $A$. In the first region, the autocatalyst is taken to decay linearly. Approximate solutions are found through the Picard iterative sequence of solutions. The space and time variations of the concentration of the species $A$ and $B$ are evaluated in the two regions. The oscillation of the concentrations in times has been observed in different locations. This phenomena is stepped out for relatively large times. Comparison between two consecutive solutions is made. The maximum error estimate is of order $10^{-3}$ for some appropriate time period. At this time level, the solutions obtained are adequate for laboratory simulation experiments to open systems. It is observed that no initiation to travelling waves occurs whenever the initial values of the concentrations of the reactant (or the autocatalysts) are not periodic.
