Almost Surely Asymptotic Stability of Numerical Solutions for Neutral Stochastic Delay Differential Equations by Zhanhua Yu, Mingzhu Liu

“…We investigate the almost surely asymptotic stability of Euler-type methods for neutral stochastic delay differential equations (NSDDEs) using the discrete semimartingale convergence theorem. …”
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Asymptotic Dichotomy in a Class of Fourth-Order Nonlinear Delay Differential Equations with Damping by Chengmin Hou, Sui Sun Cheng

“…All solutions of a fourth-order nonlinear delay differential equation are shown to converge to zero or to oscillate. …”
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A delay-differential equation model of HIV related cancer--immune system dynamics by Urszula Foryś, Jan Poleszczuk

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Numerical Integration of a Class of Singularly Perturbed Delay Differential Equations with Small Shift by Gemechis File, Y. N. Reddy

“…We have presented a numerical integration method to solve a class of singularly perturbed delay differential equations with small shift. First, we have replaced the second-order singularly perturbed delay differential equation by an asymptotically equivalent first-order delay differential equation. …”
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A novel analytical treatment for the Ambartsumian delay differential equation with a variable coefficient by Rana M. S. Alyoubi, Abdelhalim Ebaid, Essam R. El-Zahar, Mona D. Aljoufi

“…The Ambartsumian delay differential equation with a variable coefficient is considered in this paper. …”
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Stability and Bifurcation Analysis for a Delay Differential Equation of Hepatitis B Virus Infection by Xinchao Yang, Xiju Zong, Xingong Cheng, Zhenlai Han

“…The stability and bifurcation analysis for a delay differential equation of hepatitis B virus infection is investigated. …”
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Approximate Analytical Solution to Nonlinear Delay Differential Equations by Using Sumudu Iterative Method by Asfaw Tsegaye Moltot, Alemayehu Tamirie Deresse

“…Furthermore, the findings indicate that the recommended strategy is encouraging for solving other types of nonlinear delay differential equations.…”
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Investigation of fractional-order pantograph delay differential equations using Sumudu decomposition method by Asrar Saleh Alsulami, Mariam Al-Mazmumy, Maryam Ahmed Alyami, Mona Alsulami

“…This paper combines the Sumudu transform with the Adomian decomposition method to address Caputo-type fractional-order pantograph delay differential equations. It features numerical evaluations that confirm the effectiveness of the proposed methods. …”
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Necessary and sufficient conditions for the oscillation of delay differential equation with a piecewise constant argument by H. A. Agwo

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A New Technique for Solving Neutral Delay Differential Equations Based on Euler Wavelets by Mutaz Mohammad, Alexander Trounev

“…Based on the operational matrix, the neutral delay differential equations are reduced to a system of algebraic equations, which is solved through a numerical algorithm. …”
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On a class of third order neutral delay differential equations with piecewise constant argument by Garyfalos Papaschinopoulos

Subjects: “…neutral delay differential equations with piecewise constant argument…”
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On the Asymptotic Properties of Nonlinear Third-Order Neutral Delay Differential Equations with Distributed Deviating Arguments by Youliang Fu, Yazhou Tian, Cuimei Jiang, Tongxing Li

“…This paper is concerned with the asymptotic properties of solutions to a third-order nonlinear neutral delay differential equation with distributed deviating arguments. …”
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Instability of a Fifth-Order Nonlinear Vector Delay Differential Equation with Multiple Deviating Arguments by Cemil Tunç

“…We study a fifth-order nonlinear vector delay differential equation with multiple deviating arguments. …”
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A note for the global stability of a delay differential equation of hepatitis B virus infection by Bao-Zhu Guo, Li-Ming Cai

“…Kuang and J.D.Nagy,Dynamics of a delay differential equation model of hepatitis B virus infection, Journal of Biological Dynamics, 2(2008), 140-153].…”
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Parameter Dependence of Stable Invariant Manifolds for Delay Differential Equations under (μ,ν)-Dichotomies by Lijun Pan

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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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Formulation of the protein synthesis rate with sequence information by Wenjun Xia, Jinzhi Lei

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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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