University of Tabriz Computational Methods for Differential Equations 2345-3982 2 4 2014 10 01 Positivity-preserving nonstandard finite difference Schemes for simulation of advection-diffusion reaction equations 256 267 3583 EN Mohammad Mehdizadeh Khalsaraei Faculty of Mathematical Science, University of Maragheh, Maragheh, Iran Reza Shokri Jahandizi Faculty of Mathematical Science, University of Maragheh, Maragheh, Iran Journal Article 2015 02 01 Systems in which reaction terms are coupled to diffusion and advection transports arise in a wide range of chemical engineering applications, physics, biology and environmental. In these cases, the components of the unknown can denote concentrations or population sizes which represent quantities and they need to remain positive. Classical finite difference schemes may produce numerical drawbacks such as spurious oscillations and negative solutions because of truncation errors and may then become unstable. we propose a new scheme that guarantees a smooth numerical solution, free of spurious oscillations and satisfies the positivity requirement, as is demanded for the advection-diffusion reaction equations. The method is applicable to both advection and diffusion dominated problems. We give some examples from different applications. https://cmde.tabrizu.ac.ir/article_3583_bfed57f3653505f17e60608b463669be.pdf