A piecewise time-linearized method for the logistic differential equation

摘要

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, c 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.