Parabolic equations in which advection-diffusion transports are coupled to reactions terms arise in different science and engineering fields, including physical and biological systems. Usually, in practical applications the unknowns are concentration of chemical compounds or population sizes being positive also from their physical nature as well. Widely used schemes such as classical finite difference may produce numerical drawbacks such as spurious oscillations and negative values in the solution because of truncation errors and may then become unstable. By using the nonstandard finite difference (NSFD) method, a better finite difference model is constructed. The proposed NSFD scheme, guarantees the positivity of the solutions and returns spurious oscillations free, solutions.
