2014
DOI: 10.1177/1687814020922113
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Applications of Legendre spectral collocation method for solving system of time delay differential equations

Abstract: The numerical techniques are regarded as the backbone of modern research. In literature, the exact solution of time delay differential models are hardly achievable or impossible. Therefore, numerical techniques are the only way to find their solution. In this article, a novel numerical technique known as Legendre spectral collocation method is used for the approximate solution of time delay differential system. Legendre spectral collocation method and their properties are applied to determined the general proc… Show more

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Cited by 23 publications
(9 citation statements)
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“…The Legendre-Gauss (LG) quadrature together with weight function refer [29][30][31][32][33][34] is given by…”
Section: Methods Descriptionmentioning
confidence: 99%
“…The Legendre-Gauss (LG) quadrature together with weight function refer [29][30][31][32][33][34] is given by…”
Section: Methods Descriptionmentioning
confidence: 99%
“…LSCM is also used for the numerical approach of stochastic DDEs. [36][37][38] The main advantage of our proposed scheme over other available method for the model under consideration is that our method has exponential order of convergence which is the best possible rate of convergence for any numerical scheme. This means that one can get a spectral accuracy using a few collocation points.…”
Section: đ›Œmentioning
confidence: 99%
“…The spectral element method was first introduced by Lehotzky et al 35 for the stability analysis of delay differential equations (DDEs) with time‐periodic delay. LSCM is also used for the numerical approach of stochastic DDEs 36–38 . The main advantage of our proposed scheme over other available method for the model under consideration is that our method has exponential order of convergence which is the best possible rate of convergence for any numerical scheme.…”
Section: Introductionmentioning
confidence: 99%
“…These methods leverage the spectral decomposition of operators to approximate solutions in terms of basis functions, often leading to accurate and efficient computational strategies. Spectral methods have been widely applied to standard differential equations and partial differential equations (PDEs), but their adaptation to FSDDEs represents a compelling avenue of research and application 30 – 32 .…”
Section: Introductionmentioning
confidence: 99%