A novel numerical approach for solving delay differential equations arising in population dynamics

Tugba Obut; Erkan Cimen; Musa Cakir; Tugba Obut; Erkan Cimen; Musa Cakir

doi:10.3934/mmc.2023020

Mathematical Modelling and Control

2023, Volume 3, Issue 3: 233-243. doi: 10.3934/mmc.2023020

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Research article

A novel numerical approach for solving delay differential equations arising in population dynamics

1.
Department of Mathematics, Institute of Sciences, Van Yuzuncu Yil University, Van, 65080, Turkey
2.
Department of Mathematics, Faculty of Education, Van Yuzuncu Yil University, Van, 65080, Turkey
3.
Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Van, 65080, Turkey

Received: 16 January 2023 Revised: 16 January 2023 Accepted: 17 June 2023 Published: 07 September 2023

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.
- delay differential equation,
- finite difference method,
- convergence
Citation: Tugba Obut, Erkan Cimen, Musa Cakir. A novel numerical approach for solving delay differential equations arising in population dynamics[J]. Mathematical Modelling and Control, 2023, 3(3): 233-243. doi: 10.3934/mmc.2023020

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Abstract

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.

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