An efficient numerical approach for delayed logistic models

TL;DR

This paper introduces an efficient semi-analytical numerical method for solving delayed logistic models, including those with multiple delays, and compares its performance with existing methods.

Contribution

It presents a novel semi-analytical approach based on the method of steps and differential transformation for delayed logistic models, including neutral types with multiple delays.

Findings

The proposed method is validated against established numerical techniques.

Algorithms are effective for both commensurate and non-commensurate delays.

The approach demonstrates high efficiency and accuracy in numerical examples.

Abstract

In the paper an efficient semi-analytical approach based on the method of steps and differential transformation is proposed for numerical approximation of solutions of retarded logistic models of delayed and neutral type, including models with several constant delays. Algorithms for both commensurate and non-commensurate delays are described, applications are shown in examples. Validity and efficiency of the presented algorithms is compared with variational iteration method, Adomian decomposition method and polynomial least squares method numerically. Matlab package DDE23 is used to produce reference numerical values.