Numerical methods for delay differential equations

By Alfredo Bellen, Marino Zennaro. 2003

1,066 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/6181bf3cefebccc6a63fa59efa4089eb4b64c092

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In Computational Mechanics

In Numerical Analysis

Citations in the corpus

Polychronization: Computation with Spikes (2006, background): “1 For example, the simplest delay equation x � =− x(t − 1), x ∈ R has infinite dimension because to solve it, we need to specify the initial condition on the entire interval [−1, 0], and not just in the point t = 0. Delayed dynamical systems can exhibit astonishingly rich and complex dynamics (e.g.,”
A domain decomposition method for solving singularly perturbed parabolic reaction‐diffusion problems with time delay (2018, background): “Delay differential equations arise as mathematical models describing various natural phenomena in Biosciences (see [3, 4]).”
Data Based Identification and Prediction of Nonlinear and Complex Dynamical Systems (2016, methodology): “en the z-variable of one node and the x-variable of another. The time series used to reconstruct the whole network system were acquired by integrating the coupled delayed differential-equation system [262] with step size 5 10 5. The vector ﬁelds of the nodal dynamics were expanded into a power serie”
Recent trends in the numerical solution of retarded functional differential equations* (2009, methodology): “These topics are covered in the book by Bellen and Zennaro (2003) and, hence, neither proofs nor bibliographic references are given here.”
Analysis of the compact difference scheme for the semilinear fractional partial differential equation with time delay (2017, background): “has been of great interest due to the intensive development of the theory of fractional calculus and its application in various technical systems, such as automatic control,[1] traffic models,[2] population dynamics,[3] economics, and many other fields.[4,5] In the past few years, much attention has”
A SPECTRAL METHOD FOR PANTOGRAPH-TYPE DELAY DIFFERENTIAL EQUATIONS AND ITS CONVERGENCE ANALYSIS * (2009, methodology): “, the monograph [3]) and collocation methods (cf.”
Dissipativity of θ-methods for nonlinear Volterra delay-integro-differential equations (2007, neutral): “2a) and the monotonicity conditions [3,22] Re〈u1 − u2, f (u1, v, w) − f (u2, v, w)〉 a‖u1 − u2‖(2), t 0, u1, u2, v, w ∈ X, (2.”
Earthquake ruptures with thermal weakening and the operation of major faults at low overall stress levels (2009, background): “[Baker, 1996; Bellen and Zennaro, 2003] which permit evaluation of Dn(t 0) (and {qi(x, t 0)}, though this is not necessary) for any t0 in [0, t] (which permits the use of high-order quadrature rules to evaluate the functional term).”
Numerical Methods for Evolutionary Differential Equations (2008, background): “In general the delay d may be a function, it may be positive or negative, and there may be several delays [86, 22].”