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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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2020/9176784 |
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| _version_ | 1832568654660632576 |
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| author | Behrooz Basirat Hamid Reza Elahi |
| author_facet | Behrooz Basirat Hamid Reza Elahi |
| author_sort | Behrooz Basirat |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-9d822fcec6264a40be3bcddcec52826c |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-9d822fcec6264a40be3bcddcec52826c2025-02-03T00:58:41ZengWileyInternational 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2020/9176784 |
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