Discrete First-Order Three-Point Boundary Value Problem

M. Mohamed, H. B. Thompson, M. S. Jusoh, K. Jusoff


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.

Full Text:


DOI: https://doi.org/10.5539/jmr.v1n2p207

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

Copyright © Canadian Center of Science and Education

To make sure that you can receive messages from us, please add the 'ccsenet.org' domain to your e-mail 'safe list'. If you do not receive e-mail in your 'inbox', check your 'bulk mail' or 'junk mail' folders.