We compare and investigate the performance of the exact scheme of the Michaelis-Menten
(M-M) ordinary differential equation with several new non-standard finite difference (NSFD)
schemes that we construct by using Mickens’ rules. Furthermore, the exact scheme of the M-M
equation is used to design several dynamically consistent NSFD schemes for related reactiondiffusion
equations, advection-reaction equations and advection-reaction-diffusion equations.
Numerical simulations that support the theory and demonstrate computationally the power
of NSFD schemes are presented.