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...

Predator–prey systems with linear and logistic intrinsic growth rate of the prey are analyzed. The models incorporate the mutual interference between predators into the functional response which stabilizes predator–prey interactions in the system. Positive and elementary stable nonstandard...

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...