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首页> 外文期刊>International Journal of Analysis and Applications >Dhage Iteration Method for Approximating Positive Solutions of PBVPs of Nonlinear Quadratic Differential Equations with Maxima
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Dhage Iteration Method for Approximating Positive Solutions of PBVPs of Nonlinear Quadratic Differential Equations with Maxima

机译：用最大值逼近非线性二次微分方程PBVP正解的损伤迭代法。

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摘要

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.
机译：在本文中，作者证明了带极大值的一阶常非线性二次微分方程的周期边值问题的正解的存在性和逼近性。提出了一种求解算法，结果表明，在某些合适的混合混合条件下，某些连续逼近序列单调收敛于所考虑二次微分方程的正解。我们的结果依赖于Dhage（2014）最近的混合不动点定理中体现的Dhage迭代原理。还提供了一个数值示例来说明本文提出的假设和抽象理论。

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