Abstract
We first present a local convergence analysis for some families of fourth and six order methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Earlier studies have used hypotheses on the fourth Fréchet-derivative of the operator involved. We use hypotheses only on the first Fréchet-derivative in one local convergence analysis. This way, the applicability of these methods is extended. Moreover, the radius of convergence and computable error bounds on the distances involved are also given in this study based on Lipschitz constants. Numerical examples illustrating the theoretical results are also presented in this study.
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Acknowledgements
This research was partially supported by Ministerio de Economía y Competitividad under Grant MTM2014-52016-C2-1P. This research was supported by Universidad Internacional de La Rioja (UNIR, http://www.unir.net), under the Plan Propio de Investigación, Desarrollo e Innovación 3 [2015–2017]. Research group: MAPPING and by the Grant SENECA 19374/PI/14.
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Argyros, I.K., Magreñán, Á.A., Orcos, L. et al. Different methods for solving STEM problems. J Math Chem 57, 1268–1281 (2019). https://doi.org/10.1007/s10910-018-0950-1
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DOI: https://doi.org/10.1007/s10910-018-0950-1