A dynamically consistent and time-efficient numerical design for the reaction diffusion model in three space dimensions

In this study, a famous Brusselator non-linear model arising in enzymatic and triple collision is considered to analyse its various physical features. These features include positivity, stability, and convergence. To attain these features, a novel positivity-preserving non-standard finite difference (NSFD) operator splitting scheme is proposed for the investigation of a numerical solution of non-linear Brusselator model, which describes the dynamical behaviour of autocatalytic chemical reactions and a well-known minimal mathematical model for chemical oscillations. The results show that the proposed scheme is implicit in nature and efficient in time compared to explicit finite difference (FD) schemes. It also converges towards a true equilibrium point at all step sizes under a certain condition.