Euler-Maclaurin Method for Linear Differential Equations with Piecewise Constant Arguments with One Delay: Stability and Oscillations

Euler-Maclaurin Method for Linear Differential Equations with Piecewise Constant Arguments with One Delay: Stability and Oscillations

This paper focuses on the stability and oscillations of Euler-Maclaurin method for linear differential equations with piecewise constant arguments . The necessary and sufficient conditions under which the numerical stability region contains the analytical stability region are given. Furthermore, the...

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Main Authors: Qi Wang, Jiechang Wen, Shenshan Qiu
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/232484
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spelling doaj-7186e0ed21c949539b460a519365896f2020-11-24T21:44:24ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/232484232484Euler-Maclaurin Method for Linear Differential Equations with Piecewise Constant Arguments with One Delay: Stability and OscillationsQi Wang0Jiechang Wen1Shenshan Qiu2School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, ChinaSchool of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, ChinaCSIB Software Technology Center, Administrative Commission of Guangzhou Tianhe Software Park, Guangzhou 510635, ChinaThis paper focuses on the stability and oscillations of Euler-Maclaurin method for linear differential equations with piecewise constant arguments . The necessary and sufficient conditions under which the numerical stability region contains the analytical stability region are given. Furthermore, the conditions of oscillation for the Euler-Maclaurin method are obtained. We prove that the Euler-Maclaurin method preserves the oscillations of the analytic solution. Moreover, the relationships between stability and oscillations are discussed for analytic solution and numerical solution, respectively. Finally, some numerical experiments for verifying the theoretical analysis are also provided.http://dx.doi.org/10.1155/2013/232484
collection DOAJ
language English
format Article
sources DOAJ
author Qi Wang
Jiechang Wen
Shenshan Qiu
spellingShingle Qi Wang
Jiechang Wen
Shenshan Qiu
Euler-Maclaurin Method for Linear Differential Equations with Piecewise Constant Arguments with One Delay: Stability and Oscillations
Abstract and Applied Analysis
author_facet Qi Wang
Jiechang Wen
Shenshan Qiu
author_sort Qi Wang
title Euler-Maclaurin Method for Linear Differential Equations with Piecewise Constant Arguments with One Delay: Stability and Oscillations
title_short Euler-Maclaurin Method for Linear Differential Equations with Piecewise Constant Arguments with One Delay: Stability and Oscillations
title_full Euler-Maclaurin Method for Linear Differential Equations with Piecewise Constant Arguments with One Delay: Stability and Oscillations
title_fullStr Euler-Maclaurin Method for Linear Differential Equations with Piecewise Constant Arguments with One Delay: Stability and Oscillations
title_full_unstemmed Euler-Maclaurin Method for Linear Differential Equations with Piecewise Constant Arguments with One Delay: Stability and Oscillations
title_sort euler-maclaurin method for linear differential equations with piecewise constant arguments with one delay: stability and oscillations
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
description This paper focuses on the stability and oscillations of Euler-Maclaurin method for linear differential equations with piecewise constant arguments . The necessary and sufficient conditions under which the numerical stability region contains the analytical stability region are given. Furthermore, the conditions of oscillation for the Euler-Maclaurin method are obtained. We prove that the Euler-Maclaurin method preserves the oscillations of the analytic solution. Moreover, the relationships between stability and oscillations are discussed for analytic solution and numerical solution, respectively. Finally, some numerical experiments for verifying the theoretical analysis are also provided.
url http://dx.doi.org/10.1155/2013/232484
work_keys_str_mv AT qiwang eulermaclaurinmethodforlineardifferentialequationswithpiecewiseconstantargumentswithonedelaystabilityandoscillations
AT jiechangwen eulermaclaurinmethodforlineardifferentialequationswithpiecewiseconstantargumentswithonedelaystabilityandoscillations
AT shenshanqiu eulermaclaurinmethodforlineardifferentialequationswithpiecewiseconstantargumentswithonedelaystabilityandoscillations
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