EFFICIENT EXPLICIT NONSTANDARD FINITE DIFFERENCE SCHEME WITH POSITIVITY-PRESERVING PROPERTY

Abstract

Parabolic equations in which advection-diffusion transports are coupled to reactions terms
arise in different science and engineering fields, including physical and biological systems.
Usually, in practical applications the unknowns are concentration of chemical compounds or
population sizes being positive also from their physical nature as well. Widely used schemes
such as classical finite difference may produce numerical drawbacks such as spurious oscillations
and negative values in the solution because of truncation errors and may then become
unstable. By using the nonstandard finite difference (NSFD) method, a better finite difference
model is constructed. The proposed NSFD scheme, guarantees the positivity of the solutions
and returns spurious oscillations free, solutions.

Keywords

• Parabolic equations,Nonstandard finite differences; Positivity preserving.