An Improved Collocation Approach of Euler Polynomials Connected with Bernoulli Ones for Solving Predator-Prey Models with Time Lag

An Improved Collocation Approach of Euler Polynomials Connected with Bernoulli Ones for Solving Predator-Prey Models with Time Lag

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...

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Main Authors: Behrooz Basirat, Hamid Reza Elahi
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:International Journal of Differential Equations
Online Access:http://dx.doi.org/10.1155/2020/9176784
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spelling doaj-9d822fcec6264a40be3bcddcec52826c2020-11-25T02:06:28ZengHindawi LimitedInternational Journal of Differential Equations1687-96431687-96512020-01-01202010.1155/2020/91767849176784An Improved Collocation Approach of Euler Polynomials Connected with Bernoulli Ones for Solving Predator-Prey Models with Time LagBehrooz Basirat0Hamid Reza Elahi1Department of Mathematics, Birjand Branch, Islamic Azad University, Birjand, IranDepartment of Mathematics, Birjand Branch, Islamic Azad University, Birjand, IranThis 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.http://dx.doi.org/10.1155/2020/9176784
collection DOAJ
language English
format Article
sources DOAJ
author Behrooz Basirat
Hamid Reza Elahi
spellingShingle Behrooz Basirat
Hamid Reza Elahi
An Improved Collocation Approach of Euler Polynomials Connected with Bernoulli Ones for Solving Predator-Prey Models with Time Lag
International Journal of Differential Equations
author_facet Behrooz Basirat
Hamid Reza Elahi
author_sort Behrooz Basirat
title An Improved Collocation Approach of Euler Polynomials Connected with Bernoulli Ones for Solving Predator-Prey Models with Time Lag
title_short An Improved Collocation Approach of Euler Polynomials Connected with Bernoulli Ones for Solving Predator-Prey Models with Time Lag
title_full An Improved Collocation Approach of Euler Polynomials Connected with Bernoulli Ones for Solving Predator-Prey Models with Time Lag
title_fullStr An Improved Collocation Approach of Euler Polynomials Connected with Bernoulli Ones for Solving Predator-Prey Models with Time Lag
title_full_unstemmed An Improved Collocation Approach of Euler Polynomials Connected with Bernoulli Ones for Solving Predator-Prey Models with Time Lag
title_sort improved collocation approach of euler polynomials connected with bernoulli ones for solving predator-prey models with time lag
publisher Hindawi Limited
series International Journal of Differential Equations
issn 1687-9643
1687-9651
publishDate 2020-01-01
description 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.
url http://dx.doi.org/10.1155/2020/9176784
work_keys_str_mv AT behroozbasirat animprovedcollocationapproachofeulerpolynomialsconnectedwithbernoullionesforsolvingpredatorpreymodelswithtimelag
AT hamidrezaelahi animprovedcollocationapproachofeulerpolynomialsconnectedwithbernoullionesforsolvingpredatorpreymodelswithtimelag
AT behroozbasirat improvedcollocationapproachofeulerpolynomialsconnectedwithbernoullionesforsolvingpredatorpreymodelswithtimelag
AT hamidrezaelahi improvedcollocationapproachofeulerpolynomialsconnectedwithbernoullionesforsolvingpredatorpreymodelswithtimelag
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