On existence, uniqueness and numerical approximation for neutral equations with state-dependent delays

DOI10.1016/S0168-9274(97)00035-4zbMath0939.65101OpenAlexW2049847170WikidataQ127124772 ScholiaQ127124772MaRDI QIDQ1360559

Ferenc Hartung, Janos Turi, Terry L. Herdman

Publication date: 17 July 1997

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0168-9274(97)00035-4

zbMATH Keywords

convergenceexistenceuniquenessnumerical examplesone-step methodneutral functional differential equationsstate-dependent delays

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Neutral functional-differential equations (34K40)

Related Items (18)

A study of controllability of impulsive neutral evolution integro-differential equations with state-dependent delay in Banach spaces ⋮ Numerical Approximation of Neutral Differential Equations on Infinite Interval ⋮ On numerical approximation using differential equations with piecewise-constant arguments ⋮ On nonlinear Volterra integral equations with state dependent delays in several variables ⋮ Unnamed Item ⋮ Parameter Identification in a Respiratory Control System Model with Delay ⋮ Differentiability of solutions with respect to parameters in neutral differential equations with state-dependent delays ⋮ Existence results for partial neutral functional differential equations with state-dependent delay ⋮ High-order collocation methods for singular Volterra functional equations of neutral type ⋮ Approximation of mild solutions of delay integro-differential equations on Banach spaces ⋮ On differentiability of solutions with respect to parameters in neutral differential equations with state-dependent delays ⋮ Approximations of numerical method for neutral stochastic functional differential equations with Markovian switching ⋮ Linearized stability for a class of neutral functional differential equations with state-dependent delays ⋮ Approximation of mild solutions of delay differential equations on Banach spaces ⋮ Discontinuous solutions of neutral delay differential equations ⋮ Strong convergence of the split-step theta method for neutral stochastic delay differential equations ⋮ Carathéodory solutions to hyperbolic functional differential systems with state dependent delays ⋮ Unnamed Item

Cites Work

• Delay differential equations: with applications in population dynamics
• On approximation of the solutions of delay differential equations by using piecewise constant arguments
• Parameter identification in classes of hereditary systems of neutral type
• Introduction to functional differential equations
• Numerical approximations for a class of differential equations with time- and state-dependent delays
• Existence, uniqueness and continuous dependence for hereditary systems
• One-Step Methods of any Order for Neutral Functional Differential Equations
• Identification of parameters in delay equations with state-dependent delays
• Existence and Continuous Dependence for a Class of Nonlinear Neutral- Differential Equations
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