Dhage Iteration Method for Approximating Positive Solutions of PBVPs of Nonlinear Quadratic Differential Equations with Maxima
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Etamaths Publishing
2016-03-01
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| Series: | International Journal of Analysis and Applications |
| Online Access: | http://etamaths.com/index.php/ijaa/article/view/671 |
| _version_ | 1818909702581387264 |
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| author | Shyam B. Dhage Bapurao C. Dhage |
| author_facet | Shyam B. Dhage Bapurao C. Dhage |
| author_sort | Shyam B. Dhage |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-19T22:31:07Z |
| format | Article |
| id | doaj.art-7596061099124e0d8984d75635bf7077 |
| institution | Directory Open Access Journal |
| issn | 2291-8639 |
| language | English |
| last_indexed | 2024-12-19T22:31:07Z |
| publishDate | 2016-03-01 |
| publisher | Etamaths Publishing |
| record_format | Article |
| series | International Journal of Analysis and Applications |
| spelling | doaj.art-7596061099124e0d8984d75635bf70772022-12-21T20:03:21ZengEtamaths 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 |
| 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 |
| title | 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_short | 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 |
| url | http://etamaths.com/index.php/ijaa/article/view/671 |
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