Asymptotic expansion for the solution of singularly perturbed delay differential equations
TLDR
In this article, the authors extend singular perturbation theory in ordinary differential equations to delay differential equations with a fixed lag, and give an explicit sufficient condition so that the solution of a class of singularly perturbed delay differential equation can be asymptotically expanded.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 2003-05-15 and is currently open access. It has received 19 citations till now. The article focuses on the topics: Method of matched asymptotic expansions & Stochastic partial differential equation.read more
Citations
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Journal ArticleDOI
Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)
Journal ArticleDOI
A higher order difference method for singularly perturbed parabolic partial differential equations
TL;DR: In this paper, a higher order numerical method for the singularly perturbed parabolic convection-diffusion problems where the diffusion term is multiplied by a small perturbation parameter was proposed.
Journal ArticleDOI
An a posteriori based convergence analysis for a nonlinear singularly perturbed system of delay differential equations on an adaptive mesh
TL;DR: It is theoretically shown that the layer adaptive solution on the a posteriori generated mesh will uniformly converge to the exact solution with optimal order accuracy where the optimality is measured to the continuous problem discretization.
Journal ArticleDOI
On singularly perturbed small step size difference-differential nonlinear PDEs
TL;DR: In this article, a family of singularly perturbed small step size difference-differential nonlinear equations in the complex domain is studied and the authors construct formal solutions to these equations with respect to the perturbation parameter, which are asymptotic expansions with 1-Gevrey order of actual holomorphic solutions on some sectors in near the origin in.
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A finite difference scheme for a class of singularly perturbed initial value problems for delay differential equations
TL;DR: This study deals with the singularly perturbed initial value problem for a quasilinear first-order delay differential equation and generates a numerical method that is first order convergent except for a logarithmic factor in the discrete maximum norm.
References
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Book
Theory of Functional Differential Equations
TL;DR: In this paper, Liapunov functional for autonomous systems is used to define the saddle point property near equilibrium and periodic orbits for linear systems, which is a generalization of the notion of stable D operators.
Journal ArticleDOI
Oscillation and Chaos in Physiological Control Systems
Michael C. Mackey,Leon Glass +1 more
TL;DR: First-order nonlinear differential-delay equations describing physiological control systems displaying a broad diversity of dynamical behavior including limit cycle oscillations, with a variety of wave forms, and apparently aperiodic or "chaotic" solutions are studied.
Book
Differential-Difference Equations
Richard Bellman,Kenneth L. Cooke +1 more
TL;DR: In this paper, the authors introduce the study of differential difference equations and discuss some of the main features of the theory, and discuss the asymptotic behavior of solutions and the problem of stability.
Journal ArticleDOI
Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)
Journal ArticleDOI
Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system
TL;DR: In this article, the stability of the stationary state is investigated in the fast limit of the atomic relaxation for a ring cavity containing a homogeneously broadened two level absorber.
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