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 nonstandard finite difference (NSFD) schemes that we construct using Mickens' rules. Furthermore, the exact scheme of the M-M equation is used to design several dynamically consistent NSFD schemes for related reaction-diffusion 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. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 Copyright © 2012 Wiley Periodicals, Inc.