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...

The dynamics of a mathematical model of a layer of single phytoplankton species growing over a pool of nutrients, proposed by [A.H. Taylor, J.R.W. Harris, J. Aiken, The interaction of physical and biological process in a model of the vertical distribution of phytoplankton under stratification,...