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

B. C. Dhage; S. B. Dhage; S. K. Ntouyas

doi:10.26637/mjm401/002

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

Mathematics Subject Classification:

45G10, 45G99

Authors Imprint References Funding Related Articles Downloads

B. C. Dhage Kasubai, Gurukul Colony, Ahmedpur-413 515, Dist: Latur, Maharashtra, India. https://orcid.org/0000-0002-2353-8618
S. B. Dhage Kasubai, Gurukul Colony, Ahmedpur-413 515, Dist: Latur, Maharashtra, India. https://orcid.org/0000-0003-4605-5421
S. K. Ntouyas Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece.

Pages: 8-18
Date Published: 01-01-2016
Vol. 4 No. 01 (2016): Malaya Journal of Matematik (MJM)

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