Solving problems in various fields of science and engineering, such as physical and biological systems, leads to solving parabolic equations of the advectiondiffusion reaction (ADR) type. In these problems, usually the concentration of chemical compounds or the size of the population are our unknowns, which are positive in nature. In general, the use of common methods, such as the classical finite difference method, may produce numerical drawbacks such as spurious oscillations and negative values in the solutions due to truncation errors. By using the nonstandard finite difference (NSFD) method, a better finite difference model is constructed. The proposed NSFD scheme ensures that the solutions are positive and there are no spurious oscillations in the solutions.
