Legendre-Gauss Spectral Collocation Method for Second Order Nonlinear Delay Differential Equations

Wang, Lijun Yi and Zhongqing

doi:10.4208/nmtma.2014.1309nm

Cited by 6 publications

(1 citation statement)

References 9 publications

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“…For instance, Wihler [29] presented the continuous hp-Galerkin finite element time-stepping methods for the initial value problems of ODEs, Guo et al [11-15, 26, 32, 33] designed several Legendre and Laguerre spectral collocation methods for the initial value problems of ODEs, and Yang and Wang [30] proposed a Chebyshev-Gauss spectral collocation method for the initial value problems of ODEs. Besides, Wang et al [27,31,34] developed several Legendre spectral collocation methods for the nonlinear delay differential equations. The interested reader may also refer to Kanyamee and Zhang [18] and the references therein for other related works.…”

Section: Introductionmentioning

confidence: 99%

A Multiple Interval Chebyshev-Gauss-Lobatto Collocation Method for Ordinary Differential Equations

Wang

2016

Numer. Math. Theory Methods Appl.

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We introduce a multiple interval Chebyshev-Gauss-Lobatto spectral collocation method for the initial value problems of the nonlinear ordinary differential equations (ODES). This method is easy to implement and possesses the high order accuracy. In addition, it is very stable and suitable for long time calculations. We also obtain thehp-version bound on the numerical error of the multiple interval collocation method underH1-norm. Numerical experiments confirm the theoretical expectations.

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Section: Introductionmentioning

confidence: 99%

A Multiple Interval Chebyshev-Gauss-Lobatto Collocation Method for Ordinary Differential Equations

Wang

2016

Numer. Math. Theory Methods Appl.

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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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A stability preserved time-integration method for nonlinear advection–diffusion-reaction processes

Tunc

Sarı

2021

J Math Chem

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Legendre-Gauss Spectral Collocation Method for Second Order Nonlinear Delay Differential Equations

Cited by 6 publications

References 9 publications

A Multiple Interval Chebyshev-Gauss-Lobatto Collocation Method for Ordinary Differential Equations

A Multiple Interval Chebyshev-Gauss-Lobatto Collocation Method for Ordinary Differential Equations

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

A stability preserved time-integration method for nonlinear advection–diffusion-reaction processes

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