Pseudo almost periodic solutions for equation with piecewise constant argument

Dads, E. Ait; Lhachimi, Lahcen

doi:10.1016/j.jmaa.2010.06.032

Cited by 19 publications

(3 citation statements)

References 8 publications

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“…In the literature, considerable work has been done on the qualitative investigation of EPCA, including the stability , the oscillation and the periodicity , and so forth. For more information on EPCA, we refer the interested reader to and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of parabolic partial differential equations with piecewise continuous arguments

Wang

2016

Numerical Methods Partial

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This article deals with the analytic and numerical stability of numerical methods for a parabolic partial differential equation with piecewise continuous arguments of alternately retarded and advanced type. First, application of the theory of separation of variables in matrix form and the Fourier method, the necessary and sufficient condition under which the analytic solution is asymptotically stable is derived. Then, the θ‐methods are applied to solve the corresponding initial value problem, the sufficient conditions for the asymptotic stability of numerical methods are obtained. Finally, several numerical examples are presented to support the theoretical results. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 531–545, 2017

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Section: Introductionmentioning

confidence: 99%

Stability analysis of parabolic partial differential equations with piecewise continuous arguments

Wang

2016

Numerical Methods Partial

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“…For some applications of this equation we refer the interested reader to [1,[8][9][10]. Several important properties of the analytic solution of EPCA as well as numerical methods have been studied in [11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Analytical Approach to Differential Equations with Piecewise Continuous Arguments via Modified Piecewise Variational Iteration Method

Wang¹

2014

JAMP

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In the present article, we apply the modified piecewise variational iteration method to obtain the approximate analytical solutions of the differential equations with piecewise continuous arguments. This technique provides a sequence of functions which converges to the exact solution of the problem. Moreover, this method reduces the volume of calculations because it does not need discretization of the variables, linearization or small perturbations. The results seem to show that the method is very reliable and convenient for solving such equations.

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“…We have found some results in the literature that directly deal with the qualitative investigation of EPCA, including the stability , the oscillations , and the periodicity , and so forth. For further information of EPCA, the reader can see and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Analytical and numerical stability of partial differential equations with piecewise constant arguments

Wang

Wen

2013

Numerical Methods Partial

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This article is concerned with the stability analysis of the analytic and numerical solutions of a partial differential equation with piecewise constant arguments of mixed type. First, by means of the similar technique in Wiener and Debnath [Int J Math Math Sci 15 (1992), 781–788], the sufficient conditions under which the analytic solutions asymptotically stable are obtained. Then, the θ‐methods are used to solve the above‐mentioned equation, the sufficient conditions for the asymptotic stability of numerical methods are derived. Finally, some numerical experiments are given to demonstrate the conclusions.Copyright © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1‐16, 2014

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Pseudo almost periodic solutions for equation with piecewise constant argument

Abstract: By using the roughness theory of exponential dichotomies and the contraction mapping, some sufficient conditions are obtained for the existence and uniqueness of pseudo almost periodic solution of the above differential equation with piecewise constant argument

Cited by 19 publications

References 8 publications

Stability analysis of parabolic partial differential equations with piecewise continuous arguments

Stability analysis of parabolic partial differential equations with piecewise continuous arguments

Analytical Approach to Differential Equations with Piecewise Continuous Arguments via Modified Piecewise Variational Iteration Method

Analytical and numerical stability of partial differential equations with piecewise constant arguments

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