An Improved Collocation Approach of Euler Polynomials Connected with Bernoulli Ones for Solving Predator-Prey Models with Time Lag. (1st April 2020)

• Record Type: Journal Article
• Authors: Basirat, Behrooz; Elahi, Hamid Reza
• Other Names: Wong Patricia J. Y. Academic Editor.
• Is Part Of: International journal of differential equations. Volume 2020(2020)
• Publication Date: 2020-04-01
• Subjects: Differential equations -- Periodicals; Differential equations; Periodicals; 515.35
• DOI: 10.1155/2020/9176784
• Languages: English
• ISSNs: 1687-9643

Abstract

Abstract : This paper deals with an approach to obtaining the numerical solution of the Lotka–Volterra predator-prey models with discrete delay using Euler polynomials connected with Bernoulli ones. By using the Euler polynomials connected with Bernoulli ones and collocation points, this method transforms the predator-prey model into a matrix equation. The main characteristic of this approach is that it reduces the predator-prey model to a system of algebraic equations, which greatly simplifies the problem. For these models, the explicit formula determining the stability and the direction is given. Numerical examples illustrate the reliability and efficiency of the proposed scheme.