A novel numerical approach for solving delay differential equations arising in population dynamics
In this paper, the initial-value problem for a class of first order delay differential equations, which emerges as a model for population dynamics, is considered. To solve this problem numerically, using the finite difference method including interpolating quadrature rules with the basis functions,...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-09-01
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| Series: | Mathematical Modelling and Control |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mmc.2023020?viewType=HTML |
| _version_ | 1797367897438289920 |
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| author | Tugba Obut Erkan Cimen Musa Cakir |
| author_facet | Tugba Obut Erkan Cimen Musa Cakir |
| author_sort | Tugba Obut |
| collection | DOAJ |
| description | In this paper, the initial-value problem for a class of first order delay differential equations, which emerges as a model for population dynamics, is considered. To solve this problem numerically, using the finite difference method including interpolating quadrature rules with the basis functions, we construct a fitted difference scheme on a uniform mesh. Although this scheme has the same rate of convergence, it has more efficiency and accuracy compared to the classical Euler scheme. The different models, Nicolson's blowfly and Mackey–Glass models, in population dynamics are solved by using the proposed method and the classical Euler method. The numerical results obtained from here show that the proposed method is reliable, efficient, and accurate. |
| first_indexed | 2024-03-08T17:23:46Z |
| format | Article |
| id | doaj.art-727f5feb795f4005aeaaae483f206924 |
| institution | Directory Open Access Journal |
| issn | 2767-8946 |
| language | English |
| last_indexed | 2024-03-08T17:23:46Z |
| publishDate | 2023-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Modelling and Control |
| spelling | doaj.art-727f5feb795f4005aeaaae483f2069242024-01-03T01:24:12ZengAIMS PressMathematical Modelling and Control2767-89462023-09-013323324310.3934/mmc.2023020A novel numerical approach for solving delay differential equations arising in population dynamicsTugba Obut0Erkan Cimen1Musa Cakir21. Department of Mathematics, Institute of Sciences, Van Yuzuncu Yil University, Van, 65080, Turkey2. Department of Mathematics, Faculty of Education, Van Yuzuncu Yil University, Van, 65080, Turkey3. Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Van, 65080, TurkeyIn this paper, the initial-value problem for a class of first order delay differential equations, which emerges as a model for population dynamics, is considered. To solve this problem numerically, using the finite difference method including interpolating quadrature rules with the basis functions, we construct a fitted difference scheme on a uniform mesh. Although this scheme has the same rate of convergence, it has more efficiency and accuracy compared to the classical Euler scheme. The different models, Nicolson's blowfly and Mackey–Glass models, in population dynamics are solved by using the proposed method and the classical Euler method. The numerical results obtained from here show that the proposed method is reliable, efficient, and accurate.https://www.aimspress.com/article/doi/10.3934/mmc.2023020?viewType=HTMLdelay differential equationfinite difference methodconvergence |
| spellingShingle | Tugba Obut Erkan Cimen Musa Cakir A novel numerical approach for solving delay differential equations arising in population dynamics Mathematical Modelling and Control delay differential equation finite difference method convergence |
| title | A novel numerical approach for solving delay differential equations arising in population dynamics |
| title_full | A novel numerical approach for solving delay differential equations arising in population dynamics |
| title_fullStr | A novel numerical approach for solving delay differential equations arising in population dynamics |
| title_full_unstemmed | A novel numerical approach for solving delay differential equations arising in population dynamics |
| title_short | A novel numerical approach for solving delay differential equations arising in population dynamics |
| title_sort | novel numerical approach for solving delay differential equations arising in population dynamics |
| topic | delay differential equation finite difference method convergence |
| url | https://www.aimspress.com/article/doi/10.3934/mmc.2023020?viewType=HTML |
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