Nonstandard finite difference schemes for Michaelis-Menten type reaction-diffusion equations

Abstract

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.