The long time behavior of a spectral collocation method for delay differential
equations
of pantograph type

Tang, Jie; Xie, Zhongliang; Zhang, Zhimin

doi:10.3934/dcdsb.2013.18.797

Cited by 1 publication

(1 citation statement)

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“…Since solutions of the DDEs globally depend on their history due to the delay functions, a global spectral method could be considered as a natural candidate for the numerical solutions of DDEs, and thereby the application of spectral methods for DDEs has received considerable attention in recent years. Various kinds of spectral methods for DDEs were introduced and analyzed; see, for example, for a Legendre‐tau method for linear DDEs with constant delays, for Legendre spectral collocation discretizations of linear DDEs with vanishing proportional delays. For nonlinear DDEs with nonlinear delays, several Legendre spectral collocation methods were proposed and analyzed, see and the references therein.…”

Section: Introductionmentioning

confidence: 99%

An h–p version of the Chebyshev spectral collocation method for nonlinear delay differential equations

Meng

Wang

2018

Numerical Methods Partial

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We develop and analyze a spectral collocation method based on the Chebyshev-Gauss-Lobatto points for nonlinear delay differential equations with vanishing delays. We derive an a priori error estimate in the H 1 -norm that is completely explicit with respect to the local time steps and the local polynomial degrees. Several numerical examples are provided to illustrate the theoretical results. KEYWORDS h-p version, Chebyshev-Gauss-Lobatto points, nonlinear delay differential equations, spectral collocation method 1 where the delay function satisfying the following conditions:We always assume that f is chosen such that the problem (1.1) possesses a unique solution u ∈ C 1 (I). In particular, the problem (1.1) includes a special important case when (t) = qt (0 < q < 1) is a linear proportional delay function satisfying (C1) and (C2).DDEs arise in many areas of mathematical modelings. During the past few decades, many numerical methods have been proposed and studied for the DDEs; see, for example, the collocation Numer Methods Partial Differential Eq. 2019;35:664-680. wileyonlinelibrary.com/journal/num

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Section: Introductionmentioning

confidence: 99%