Stability and asymptotic behavior of a numerical solution corresponding to a diffusion-reaction equation solved by a finite difference scheme (Crank-Nicolson)

Abstract In this paper some partial differential equations arising in biochemistry are studied from the numerical point of view. These nonlinear equations (based on diffusion-reaction processes) are solved by using a Crank-Nicolson technique and convergence is proved by using lower and upper solutions. Stability and asymptotic behavior are also examined. A numerical algorithm has been deduced and is presently used by chemists.