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International Journal of Engineering Mathematics
Volume 2017 (2017), Article ID 2783682, 21 pages
Research Article

A New Iterative Numerical Continuation Technique for Approximating the Solutions of Scalar Nonlinear Equations

IFSTTAR, Aix-Marseille Université, LBA UMR T24, 13016 Marseille, France

Correspondence should be addressed to Grégory Antoni; rf.oohay@yrogerg.inotna

Received 30 June 2016; Accepted 24 October 2016; Published 16 January 2017

Academic Editor: Yurong Liu

Copyright © 2017 Grégory Antoni. 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.


The present study concerns the development of a new iterative method applied to a numerical continuation procedure for parameterized scalar nonlinear equations. Combining both a modified Newton’s technique and a stationary-type numerical procedure, the proposed method is able to provide suitable approximate solutions associated with scalar nonlinear equations. A numerical analysis of predictive capabilities of this new iterative algorithm is addressed, assessed, and discussed on some specific examples.