Dhage Iteration Method for Approximating Positive Solutions of PBVPs of Nonlinear Quadratic Differential Equations with Maxima

Dhage Iteration Method for Approximating Positive Solutions of PBVPs of Nonlinear Quadratic Differential Equations with Maxima

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In this paper authors prove the existence as well as approximation of the positive solutions for a periodic boundary value problem of first order ordinary nonlinear quadratic differential equations with maxima. An algorithm for the solutions is developed and it is shown that certain sequence of succ...

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Main Authors: Shyam B. Dhage, Bapurao C. Dhage
Format: Article
Language:English
Published: Etamaths Publishing 2016-03-01
Series:International Journal of Analysis and Applications
Online Access:http://etamaths.com/index.php/ijaa/article/view/671
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spelling doaj-7596061099124e0d8984d75635bf70772021-08-26T13:44:37ZengEtamaths PublishingInternational Journal of Analysis and Applications2291-86392016-03-01102101111167Dhage Iteration Method for Approximating Positive Solutions of PBVPs of Nonlinear Quadratic Differential Equations with MaximaShyam B. Dhage0Bapurao C. Dhage1kasubai, Gurukul Colony, AhmedpurKasubai, Gurukul Colony, AhmedpurIn this paper authors prove the existence as well as approximation of the positive solutions for a periodic boundary value problem of first order ordinary nonlinear quadratic differential equations with maxima. An algorithm for the solutions is developed and it is shown that certain sequence of successive approximations converges monotonically to the positive solution of considered quadratic differential equations under some suitable mixed hybrid conditions. Our results rely on the Dhage iteration principle embodied in a recent hybrid fixed point theorem of Dhage (2014). A numerical example is also provided to illustrate the hypotheses and abstract theory developed in this paper.http://etamaths.com/index.php/ijaa/article/view/671
collection DOAJ
language English
format Article
sources DOAJ
author Shyam B. Dhage
Bapurao C. Dhage
spellingShingle Shyam B. Dhage
Bapurao C. Dhage
Dhage Iteration Method for Approximating Positive Solutions of PBVPs of Nonlinear Quadratic Differential Equations with Maxima
International Journal of Analysis and Applications
author_facet Shyam B. Dhage
Bapurao C. Dhage
author_sort Shyam B. Dhage
title Dhage Iteration Method for Approximating Positive Solutions of PBVPs of Nonlinear Quadratic Differential Equations with Maxima
title_short Dhage Iteration Method for Approximating Positive Solutions of PBVPs of Nonlinear Quadratic Differential Equations with Maxima
title_full Dhage Iteration Method for Approximating Positive Solutions of PBVPs of Nonlinear Quadratic Differential Equations with Maxima
title_fullStr Dhage Iteration Method for Approximating Positive Solutions of PBVPs of Nonlinear Quadratic Differential Equations with Maxima
title_full_unstemmed Dhage Iteration Method for Approximating Positive Solutions of PBVPs of Nonlinear Quadratic Differential Equations with Maxima
title_sort dhage iteration method for approximating positive solutions of pbvps of nonlinear quadratic differential equations with maxima
publisher Etamaths Publishing
series International Journal of Analysis and Applications
issn 2291-8639
publishDate 2016-03-01
description In this paper authors prove the existence as well as approximation of the positive solutions for a periodic boundary value problem of first order ordinary nonlinear quadratic differential equations with maxima. An algorithm for the solutions is developed and it is shown that certain sequence of successive approximations converges monotonically to the positive solution of considered quadratic differential equations under some suitable mixed hybrid conditions. Our results rely on the Dhage iteration principle embodied in a recent hybrid fixed point theorem of Dhage (2014). A numerical example is also provided to illustrate the hypotheses and abstract theory developed in this paper.
url http://etamaths.com/index.php/ijaa/article/view/671
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AT bapuraocdhage dhageiterationmethodforapproximatingpositivesolutionsofpbvpsofnonlinearquadraticdifferentialequationswithmaxima
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