Approximating solutions of nonlinear second order ordinary differential equations via Dhage iteration principle

B. C. Dhagea,* S. B. Dhagea and S. K. Ntouyasb,c

Approximating solutions of nonlinear second order ordinary differential equations via Dhage iteration principle

Authors :

B. C. Dhage^a,* S. B. Dhage^aand S. K. Ntouyas^b,c

Author Address :

^aKasubai, Gurukul Colony, Ahmedpur-413 515, Dist: Latur, Maharashtra, India.
^bDepartment of Mathematics, University of Ioannina, 451 10 Ioannina, Greece;
^cNonlinear Analysis and Applied Mathematics (NAAM)-Research Group at King Abdulaziz University, Jeddah, Saudi Arabia.

*Corresponding author.

Abstract :

In this paper the authors prove algorithms for the existence as well as approximation of the solutions for an initial and a periodic boundary value problem of nonlinear second order ordinary differential equations. The main results rely on the Dhage iteration principle embodied in a recent hybrid fixed point theorem of Dhage (2013) in the partially ordered normed linear spaces and the numerical solution of the considered equations is obtained under weaker mixed partial continuity and partial Lipschitz conditions. Our hypotheses and results are also illustrated by some numerical examples.

Keywords :

Approximating solutions, Dhage iteration principle, hybrid fixed point theorem, initial value problems, periodic boundary value problems.

DOI :

Article Info :

Received : March 25, 2015; Accepted : August 23, 2015.