Solutions of neutral delay differential equations using a generalized Lambert W function

Jamilla, Cristeta U.; Mendoza, Renier; Mező, István

doi:10.1016/j.amc.2020.125334

Cited by 15 publications

(21 citation statements)

References 44 publications

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“…This model involves a neutral delay differential equation (NDDE), which is a differential equation with delay both in state and the derivative. NDDEs have been used in modeling various applications in science and engineering [113]- [119].…”

Section: B Estimating Parameters Of a Pendulum-mass-spring-damper Systemmentioning

confidence: 99%

Philippine Eagle Optimization Algorithm

2022

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We propose the Philippine Eagle Optimization Algorithm (PEOA), which is a meta-heuristic and population-based search algorithm inspired by the territorial hunting behavior of the Philippine Eagle. From an initial random population of eagles in a given search space, the best eagle is selected and undergoes a local food search using the interior point method as its means of exploitation. The population is then divided into three subpopulations, and each subpopulation is assigned an operator which aids in the exploration. Once the respective operators are applied, the new eagles with improved function values replace the older ones. The best eagle of the population is then updated and conducts a local food search again. These steps are done iteratively, and the food searched by the final best eagle is the optimal solution of the search space. PEOA is tested on 20 optimization test functions with different modality, separability, and dimension properties. The performance of PEOA is compared to 13 other optimization algorithms. To further validate the effectiveness of PEOA, it is also applied to image reconstruction in electrical impedance tomography and parameter identification in a neutral delay differential equation model. Numerical results show that PEOA can obtain accurate solutions to various functions and problems. PEOA proves to be the most computationally inexpensive algorithm relative to the others examined, while also helping promote the critically endangered Philippine Eagle.

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Section: B Estimating Parameters Of a Pendulum-mass-spring-damper Systemmentioning

confidence: 99%

Philippine Eagle Optimization Algorithm

2022

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“…In this paper, we deal with a mathematical model that is based on system of differential equations with discrete time delay [17,32,60,72,[95][96][97]. There are different numerical methods to deal with this type of equations, and some are analogous to the ones used for ordinary differential equations but with additional issues [50,[98][99][100][101][102]. One particular numerical method that we are interested in is by using NSFD schemes to guarantee some properties of the continuous mathematical model.…”

Section: Design Of a Nsfd Scheme For The Mathematical Modelmentioning

confidence: 99%

Mathematical Analysis and Numerical Solution of a Model of HIV with a Discrete Time Delay

et al. 2021

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We propose a mathematical model based on a set of delay differential equations that describe intracellular HIV infection. The model includes three different subpopulations of cells and the HIV virus. The mathematical model is formulated in such a way that takes into account the time between viral entry into a target cell and the production of new virions. We study the local stability of the infection-free and endemic equilibrium states. Moreover, by using a suitable Lyapunov functional and the LaSalle invariant principle, it is proved that if the basic reproduction ratio is less than unity, the infection-free equilibrium is globally asymptotically stable. In addition, we designed a non-standard difference scheme that preserves some relevant properties of the continuous mathematical model.

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“…With more and more research on delay differential equations [1][2][3][4][5], it has been widely used in various fields, such as population research [6,7], epidemiology [8,9], electrodynamics [10,11], neural network system [12,13] and so on. As a special class of delay differential equations, differential equations with piecewise constant arguments (EPCA) are difficult to solve accurately because of their complex structure.…”

Section: Introductionmentioning

confidence: 99%

Numerical Stability of Runge-Kutta Methods for Differential Equations with Piecewise Constant Arguments with Matrix Coefficients

Yin

Wang

2022

Universal Journal of Mathematics and Applications

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The paper discusses the analytical stability and numerical stability of differential equations with piecewise constant arguments with matrix coefficients. It is proved that the Runge-Kutta method can keep the convergence order. The recurrence relation of the Runge-Kutta method applied to the equations is obtained. Then, the stability conditions of the numerical solution under different matrix coefficients are given by Pade approximation and order star theory. Finally, the conclusions are verified by several numerical experiments.

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Solutions of neutral delay differential equations using a generalized Lambert W function

Cited by 15 publications

References 44 publications

Philippine Eagle Optimization Algorithm

Philippine Eagle Optimization Algorithm

Mathematical Analysis and Numerical Solution of a Model of HIV with a Discrete Time Delay

Numerical Stability of Runge-Kutta Methods for Differential Equations with Piecewise Constant Arguments with Matrix Coefficients

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