A note on a positivity preserving nonstandard finite difference scheme for a modified parabolic reaction–advection–diffusion PDE

Abstract

Using the nonstandard finite difference (NSFD) scheme methodology, we construct a discretization for a parabolic partial differential equation (PDE) having linear advection and diffusion, but with a nonlinear reaction term. The most important requirement is that the scheme produces only non-negative solutions. We show that this can be achieved, and as a consequence, a functional relationship exists between space and time step-sizes. The details of the various term by term NSFD discretizations are discussed.