A piecewise time-linearized method for the logistic differential equation

A piecewise time-linearized technique is employed to determine an approximate, analytical solution to the logistic differential equation. This technique yields a nonlinear map or difference equation which preserves the fixed points and linear stability of the logistic differential equation. It is shown that this map is continuous and piecewise differentiable, coincides with that of the Euler forward method for small time steps, and differs from the predictor-corrector method proposed by Certaine and Adomian's decomposition technique. (C) 1998 Elsevier Science Inc. All rights reserved.