Advancing numerical solutions for a system of singularly perturbed delay differential equations at linear rate by Dany Joy, Dinesh Kumar S, Fathalla A Rihan

“…Abstract This work introduces a numerical technique designed to efficiently solve a specific type of differential equations known as a weakly coupled system of singularly perturbed delay differential equations. The innovation of this approach stems from its unique integration of three key elements: the Numerov method, known for its accuracy in solving second-order ODEs; a fitting factor, which improves handling of the singular perturbation parameter essential for accurately modeling SPDDEs; and the Taylor series expansion, which approximates first-order derivative terms, facilitating the application of the Numerov method to the system. …”
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Some Stability and Convergence of Additive Runge-Kutta Methods for Delay Differential Equations with Many Delays by Haiyan Yuan, Jingjun Zhao, Yang Xu

“…This paper is devoted to the stability and convergence analysis of the additive Runge-Kutta methods with the Lagrangian interpolation (ARKLMs) for the numerical solution of a delay differential equation with many delays. GDN stability and D-Convergence are introduced and proved. …”
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New Oscillation Criteria for Second-Order Neutral Delay Differential Equations with Positive and Negative Coefficients by Yuzhen Bai, Lihua Liu

“…We establish the oscillation and asymptotic criteria for the second-order neutral delay differential equations with positive and negative coefficients having the forms [x(t)+∑i∈Rci(t)x(αi(t))]′′+r(t)[x(t)+∑i∈Rci(t)x(αi(t))]′+∑i∈Ppi(t)x(βi(t))-∑i∈Qqi(t)x(γi(t))=0 and [x(t)+∑i∈Rci(t)x(αi(t))]′′+r(t)[x(t)+∑i∈Rci(t)x(αi(t))]′+∑i∈Ppi(t)x(βi(t))-∑i∈Qqi(t)x(γi(t))=f(t). …”
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New oscillation criteria for third order nonlinear functional differential equations by John Graef, Said Grace, Gokula Chhatria

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Approximate Solutions of Delay Differential Equations with Constant and Variable Coefficients by the Enhanced Multistage Homotopy Perturbation Method by D. Olvera, A. Elías-Zúñiga, L. N. López de Lacalle, C. A. Rodríguez

“…We expand the application of the enhanced multistage homotopy perturbation method (EMHPM) to solve delay differential equations (DDEs) with constant and variable coefficients. …”
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Almost Sure and Lp Convergence of Split-Step Backward Euler Method for Stochastic Delay Differential Equation by Qian Guo, Xueyin Tao

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A Robust Weak Taylor Approximation Scheme for Solutions of Jump-Diffusion Stochastic Delay Differential Equations by Yanli Zhou, Yonghong Wu, Xiangyu Ge, B. Wiwatanapataphee

“…Stochastic delay differential equations with jumps have a wide range of applications, particularly, in mathematical finance. …”
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Stability, Boundedness, and Existence of Periodic Solutions to Certain Third-Order Delay Differential Equations with Multiple Deviating Arguments by A. T. Ademola, B. S. Ogundare, M. O. Ogundiran, O. A. Adesina

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Delay differential equations via the matrix lambert w function and bifurcation analysis: application to machine tool chatter by Sun Yi, Patrick W. Nelson, A. Galip Ulsoy

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On Mean Square Stability and Dissipativity of Split-Step Theta Method for Nonlinear Neutral Stochastic Delay Differential Equations by Haiyan Yuan, Jihong Shen, Cheng Song

“…A split-step theta (SST) method is introduced and used to solve the nonlinear neutral stochastic delay differential equations (NSDDEs). The mean square asymptotic stability of the split-step theta (SST) method for nonlinear neutral stochastic delay differential equations is studied. …”
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Formulation of the protein synthesis rate with sequence information by Wenjun Xia, Jinzhi Lei

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The Semimartingale Approach to Almost Sure Stability Analysis of a Two-Stage Numerical Method for Stochastic Delay Differential Equation by Qian Guo, Xueyin Tao

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Mean-Square Convergence of Drift-Implicit One-Step Methods for Neutral Stochastic Delay Differential Equations with Jump Diffusion by Lin Hu, Siqing Gan

“…A class of drift-implicit one-step schemes are proposed for the neutral stochastic delay differential equations (NSDDEs) driven by Poisson processes. …”
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Modelling periodic oscillations during somitogenesis by Peng Feng, Menaka Navaratna

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On the interaction between the immune system and an exponentially replicating pathogen by Alberto d'Onofrio

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Bacteriophage-resistant and bacteriophage-sensitive bacteria in a chemostat by Zhun Han, Hal L. Smith

Subjects: “…delay differential equations.…”
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Some fixed point results with the vector degree of nondensifiability in generalized Banach spaces and application on coupled Caputo fractional delay differential equations by Laksaci Noura, Hasan Fady, Boudaoui Ahmed, Mustafa Zead, Shatanawi Wasfi

Subjects: “…coupled caputo fractional delay differential equations…”
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A stage structured model for mosquito suppression with immigration by Mugen Huang, Zifeng Wang, Zixin Nie

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Modeling transcriptional co-regulation of mammalian circadian clock by Yanqin Wang, Xin Ni, Jie Yan, Ling Yang

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Estimation of parameters for the stochastic linear delay growth law through the L1 distance procedure by Petras Rupšys

Subjects: “…stochastic delay differential equation…”
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