There are bacteria that can form strong biofilms in porous media. These biofilms can be used as biobarriers to restrict the flow of pollutants. For certain contaminants, a second species of bacteria that can actually react with the contaminants can be added to the biobarrier to actually degrade...

In this paper we formulate conditions that guarantee second-order accuracy of the one-step nonstandard finite difference methods for general first order autonomous ordinary differential equations. We also develop a new class of nonstandard finite-difference methods for differential equations of...