Advance-delay differential-difference equations

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Systems of advance-delay differential-difference equations and transformation groups

Electronic Journal of Differential Equations, 2016
A linear system of mixed-type differential difference equations is studied. A step derivation method and some conditions on an initial function are used to guarantee existence, uniqueness and smoothness of the solution.
Serguei I. Iakovlev, Valentina Iakovleva
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Exponentially fitted tension spline method for singularly perturbed differential difference equations [PDF]

Iranian Journal of Numerical Analysis and Optimization, 2021
In this article, singularly perturbed differential difference equations having delay and advance in the reaction terms are considered. The highest-order derivative term of the equation is multiplied by a perturbation parameter ε taking arbitrary values ...
M.M. Woldaregay, G.F. Duressa
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A Parameter Uniform Numerical Scheme for Singularly Perturbed Differential-difference Equations with Mixed Shifts [PDF]

Journal of Applied and Computational Mechanics, 2020
In this paper, we consider a second-order singularly perturbed differential-difference equations with mixed delay and advance parameters. At first, we approximate the model problem by an upwind finite difference scheme on a Shishkin mesh.
P. Mushahary, S. R. Sahu, J. Mohapatra
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Fitted Numerical Scheme for Second-Order Singularly Perturbed Differential-Difference Equations with Mixed Shifts

Abstract and Applied Analysis, 2021
This paper presents the study of singularly perturbed differential-difference equations of delay and advance parameters. The proposed numerical scheme is a fitted fourth-order finite difference approximation for the singularly perturbed differential ...
Meku Ayalew +2 more
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Stability Analysis of a Class of Neural Networks with State-Dependent State Delay

Discrete Dynamics in Nature and Society, 2020
The differential equations with state-dependent delay are very important equations because they can describe some problems in the real world more accurately. Due to the complexity of state-dependent delay, it also brings challenges to the research.
Yue Chen, Jin-E Zhang
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Non-Polynomial Spline for Singularly Perturbed Differential-Difference Equation with Mixed Shifts and Layer Behavior [PDF]

International Journal of Mathematical, Engineering and Management Sciences
Various physical phenomena give rise to singularly perturbed differential equations with mixed shifts. Due to multiple parameters, singularly perturbed mixed delay boundary value problems are challenging to solve.
Shilpa Malge , Ram Kishun Lodhi
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Non-polynomial spline method for singularly perturbed differential difference equations with delay and advance terms

Қарағанды университетінің хабаршысы. Математика сериясы
In this study, we introduced a non-polynomial spline technique to address singularly perturbed differential difference equations involving both delay and advanced parameters.
A.M. Regal, S.D. Kumar
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A Second Order Convergence Method for Differential Difference Equation with Mixed Shifts using Mixed Non-Polynomial Spline

Қарағанды университетінің хабаршысы. Математика сериясы
A proposed numerical approximation method is presented for solving a singularly perturbed second-order differential-difference equation with both the delay and advance shifts.
D. Swarnakar +3 more
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A Hybrid Fitted Mesh Numerical Scheme for Solving Singularly Perturbed Reaction–Diffusion Equation With Mixed Shifts

Journal of Mathematics
This study develops a robust hybrid numerical scheme for a class of time-dependent, singularly perturbed differential-difference equations characterized by a small positive parameter multiplying the highest order derivative term and mixed spatial shifts (
Ababi H. Ejere +3 more
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Active Inference and Functional Parametrisation: Differential Flatness and Smooth Random Realisation. [PDF]

Entropy (Basel)
Mounier H, Parr T, Friston K.
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mathematics