In this article, efficient numerical schemes for the two dimensional Gray Scott model are presented. The Gray Scott model presents self-replicating patterns such as spots and strips. These pattern formulations are suitable interplay between diffusion and reactions in which the coupled partial differential system is solved by using three finite difference schemes to enhance accuracy while maintaining stability of the system. The stability analysis is performed on stationary points whereas the analytical solution is compared with the numerical schemes, such as Douglas implicit fourth and sixth order compact difference schemes. The later two schemes are implemented for first time on such a system for analyzing error residuals and system efficiency. It is predicted that the efficiency is upgraded by Thomas block tridiagonal solver, which leads to an excellent improvement in accuracy measured by L∞ norm.