Numerical treatment of Gray-Scott model with operator splitting method

This article focuses on the numerical solution of a classical, irreversible Gray Scott reaction-diffusion system describing kinetics simple autocatalytic reaction in an unstirred ow reactor. A novel finite element scheme based B-spline collocation method is developed to solve this model. Before applying method, "strang splitting" idea especially popularized for PDEs has been applied Then, using underlying behind approximation, domain integration partitioned into subintervals which sought as basis approximate solution. Thus, partial derivatives are transformed algebraic equations. Applicability and accuracy justified via comparison with exact calculating both error norms \begin{document}$ L_2 $\end{document} id="M2">\begin{document}$ L_\infty $\end{document}. Numerical results arising from simulation experiments also presented.