Numerical modeling of three dimensional Brusselator reaction diffusion system

In many mathematical models, positivity is one of the attributes that must be possessed by the continuous systems. For instance, the unknown quantities in the Brusselator reaction-diffusion model represent the concentration of two reactant species. The negative values of concentration produced by any numerical methods is meaningless. This work is concerned with the investigation of a novel unconditionally positivity preserving finite difference (FD) scheme to be used for the solution of three dimensional Brusselator reaction-diffusion system. Von Neumann stability method and Taylor series expansion is applied to verify unconditional stability and consistency of the proposed FD scheme. Results are compared against well-known forward Euler FD scheme and some results reported in the literature.