Wave simulations of Gray-Scott reaction-diffusion system

In this work, we study the numerical simulation of the one-dimensional reaction-diffusion system known as the Gray-Scott model. This model is responsible for the spatial pattern formation, which we often meet in nature as the result of some chemical reactions. We have used the trigonometric quartic B-spline (T4B) functions for space discretization with the Crank-Nicolson method for time integration to integrate the nonlinear reaction-diffusion equation into a system of algebraic equations. The solutions of the Gray-Scott model are presented with different wave simulations. Test problems are chosen from the literature to illustrate the stationary waves, pulse-splitting waves, and self-replicating waves.