The present paper proposes a new monotone iteration method for existence as well as approximation of the coupled solutions for a coupled periodic boundary value problem of first order ordinary nonlinear differential equations. A new hybrid coupled fixed point theorem involving the Dhage iteration principle is proved in a partially ordered normed linear space and applied to the coupled periodic boundary value problems for proving the main existence and approximation results of this paper. An algorithm for the coupled solutions is developed and it is shown that the sequences of successive approximations defined in a certain way converge monotonically to the coupled solutions of the related  differential equations under some suitable mixed hybrid conditions. A numerical example is also indicated to illustrate the abstract theory developed in the paper.

Keywords: Coupled Periodic boundary value problems, Coupled fixed point theorem, Dhage iteration principle, Approximate coupled solutions