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Nonlinear Homotopic Continuation Methods: A Chemical Engineering Perspective Review

Author:
Jiménez-Islas, Hugo, Martínez-González, Gloria M., Navarrete-Bolaños, José L., Botello-Álvarez, José E., Oliveros-Muñoz, J. Manuel
Source:
Industrial & Engineering Chemistry Research 2013 v.52 no.42 pp. 14729-14742
ISSN:
1520-5045
Subject:
chemical engineering, chemistry, mathematical theory, sustainable engineering, topology
Abstract:
It is difficult to imagine mathematics or engineering to date without nonlinear algebraic systems; these topics have deserved more diverse and vigorous interest over the years. In fact, one of the most important modern branches of mathematics originated in this context, topology, which has been inseparable from homotopy theory, describes a powerful intuitive tool to solve nonlinear algebraic systems. In the present work, we attempt to briefly summarize the theoretical beginnings of homotopy, its eventual transformation into a numerical method, its most reiterative applications in chemical engineering, and some current challenges in this field from an engineering-friendly perspective, especially approachable for chemical engineers.
Agid:
5375964