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Discrete first-order three-point boundary value problem


Citation

Mohamed, Mesliza and Thompson, Bevan and Jusoh, Muhammad Sufian and Jusoff, Kamaruzaman (2009) Discrete first-order three-point boundary value problem. Journal of Mathematics Research, 1 (2). pp. 207-215. ISSN 1916-9795; ESSN: 1916-9809

Abstract

We study difference equations which arise as discrete approximations to three-point boundary value problems for systems of first-order ordinary differential equations. We obtain new results of the existence of solutions to the discrete problem by employing Euler’s method. The existence of solutions are proven by the contraction mapping theorem and the Brouwer fixed point theorem in Euclidean space. We apply our results to show that solutions to the discrete problem converge to solutions of the continuous problem in an aggregate sense. We also give some examples to illustrate the existence of a unique solution of the contraction mapping theorem.


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Additional Metadata

Item Type: Article
Divisions: Faculty of Forestry
DOI Number: https://doi.org/10.5539/jmr.v1n2p207
Publisher: Canadian Center of Science and Education
Keywords: Discrete three-point boundary value problem; Contraction mapping theorem; Brouwer fixed point theorem
Depositing User: Norhazura Hamzah
Date Deposited: 09 Jan 2014 04:10
Last Modified: 14 Jul 2020 04:27
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.5539/jmr.v1n2p207
URI: http://psasir.upm.edu.my/id/eprint/14086
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