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Open AccessArticle

Stability Anomalies of Some Jacobian-Free Iterative Methods of High Order of Convergence

1
Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 València, Spain
2
Instituto Tecnológico de Santo Domingo, Avda. Los Próceres 49, Santo Domingo 10602, Dominican Republic
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Axioms 2019, 8(2), 51; https://doi.org/10.3390/axioms8020051
Received: 22 February 2019 / Revised: 11 April 2019 / Accepted: 19 April 2019 / Published: 25 April 2019
In this manuscript, we design two classes of parametric iterative schemes to solve nonlinear problems that do not need to evaluate Jacobian matrices and need to solve three linear systems per iteration with the same divided difference operator as the coefficient matrix. The stability performance of the classes is analyzed on a quadratic polynomial system, and it is shown that for many values of the parameter, only convergence to the roots of the problem exists. Finally, we check the performance of these methods on some test problems to confirm the theoretical results. View Full-Text
Keywords: nonlinear systems; real multidimensional dynamics; stability nonlinear systems; real multidimensional dynamics; stability
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Cordero, A.; Maimó, J.G.; Torregrosa, J.R.; Vassileva, M.P. Stability Anomalies of Some Jacobian-Free Iterative Methods of High Order of Convergence. Axioms 2019, 8, 51.

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