Division of Applied Mathematics and Mechanics, Department of Engineering Sciences, University of Patras, 26500 Patras, Greece
Copyright © 2010 Eugenia N. Petropoulou. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A discrete equivalent and not analogue of the well-known logistic differential
equation is proposed. This discrete equivalent logistic equation
is of the Volterra convolution type, is obtained by use of a functional-analytic
method, and is explicitly solved using the -transform method. The connection
of the solution of the discrete equivalent logistic equation with the
solution of the logistic differential equation is discussed. Also, some differences
of the discrete equivalent logistic equation and the well-known
discrete analogue of the logistic equation are mentioned. It is hoped that
this discrete equivalent of the logistic equation could be a better choice
for the modelling of various problems, where different versions of known
discrete logistic equations are used until nowadays.