Approximating Coupled Solutions of Coupled PBVPs of Non- linear First Order Ordinary Differential Equations.

DHAGE, BAPURAO CHANDRABHAN

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.

DIFFERENTIAL equations; MONOTONE operators; NONLINEAR difference equations; SUCCESSIVE approximation analog-to-digital converters; NUMERICAL analysis

Kyungpook Mathematical Journal, 2016, Vol 56, Issue 1, p221

1225-6951

Academic Journal

10.5666/KMJ.2016.56.1.221