Table of Contents
International Journal of Engineering Mathematics
Volume 2013, Article ID 768474, 11 pages
http://dx.doi.org/10.1155/2013/768474
Research Article

Interval Arithmetic for Nonlinear Problem Solving

Department of Materials Science and Engineering, Institute of Technology of Costa Rica, Cartago 07050, Costa Rica

Received 10 February 2013; Accepted 19 May 2013

Academic Editor: A. Nazli Gundes

Copyright © 2013 Benito A. Stradi-Granados. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Implementation of interval arithmetic in complex problems has been hampered by the tedious programming exercise needed to develop a particular implementation. In order to improve productivity, the use of interval mathematics is demonstrated using the computing platform INTLAB that allows for the development of interval-arithmetic-based programs more efficiently than with previous interval-arithmetic libraries. An interval-Newton Generalized-Bisection (IN/GB) method is developed in this platform and applied to determine the solutions of selected nonlinear problems. Cases 1 and 2 demonstrate the effectiveness of the implementation applied to traditional polynomial problems. Case 3 demonstrates the robustness of the implementation in the case of multiple specific volume solutions. Case 4 exemplifies the robustness and effectiveness of the implementation in the determination of multiple critical points for a mixture of methane and hydrogen sulfide. The examples demonstrate the effectiveness of the method by finding all existing roots with mathematical certainty.