Nonstandard finite differences (NSFD) schemes can improve the accuracy and reduce computational costs of traditional finite difference methods. In addition, NSFDs produce numerical solutions which also exhibit essential properties of the solution. In this paper, we introduce a family of explicit finite difference schemes based on Mickens’ rules to approximate positive solutions of advection-diffusion equation (ADE). The proposed modification of classical scheme improves the accuracy and guarantees the positivity requirement, as is demanded for the solution of the ADE. Numerical simulations on one-dimensional advection-diffusion are used for illustrating the accuracy and performance of the proposed scheme as a compared to standard finite difference schemes.
