Approximating positive solutions of PBVPs 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 a periodic boundary 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. Our results rely on the Dhage iteration principle embodied in a recent hybrid fixed point theorem of Dhage (2014) in partially ordered normed linear spaces. A numerical example is also provided to illustrate the abstract theory developed in the paper.