Approximating positive solutions of nonlinear first order ordinary quadratic differential equations
In this paper, the authors prove the existence as well as approximations of the positive solutions for an initial value problem of first-order ordinary nonlinear quadratic differential equations. An algorithm for the solutions is developed and it is shown that the sequence of successive approximatio...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2015-12-01
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| Series: | Cogent Mathematics |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/23311835.2015.1023671 |
| Summary: | In this paper, the authors prove the existence as well as approximations of the positive solutions for an initial value problem of first-order ordinary nonlinear quadratic differential equations. An algorithm for the solutions is developed and it is shown that the sequence of successive approximations converges monotonically to the positive solution of related quadratic differential equations under some suitable mixed hybrid conditions. We base our results on the Dhage iteration method embodied in a recent hybrid fixed-point theorem of Dhage (2014) in partially ordered normed linear spaces. An example is also provided to illustrate the abstract theory developed in the paper. |
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| ISSN: | 2331-1835 |