Abstract
In this paper, we deal with the study of convergence analysis of modified parameter based family of second derivative free continuation method for solving nonlinear equations. We obtain the order of convergence is at least five and especially, for parameter \(\alpha =2\) sixth order convergence. Some application such as Max Planck’s conservative law, multi-factor effect are discussed and demonstrate the efficiency and performance of the new method (for \(\alpha =2\)). We compare the absolutely value of function at each iteration \(|f(x_n)|\) and \(|x_n-\xi |\) with our method and Potra and Pták method [1], Kou et al. method [2]. We observed that our method is more efficient than existing methods. Also, the Dynamics of the method are studied for a special case of the parameter in convergence.
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Á. A. Magreñán, Í. Sarría: The research of this author 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: Modelación matemática aplicada a la ingeniería (MOMAIN), by the Grant SENECA 19374/PI/14 and by Ministerio de Ciencia y Tecnología MTM2014-52016-C2-01-P.
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Maroju, P., Magreñán, Á.A., Motsa, S.S. et al. Second derivative free sixth order continuation method for solving nonlinear equations with applications. J Math Chem 56, 2099–2116 (2018). https://doi.org/10.1007/s10910-018-0868-7
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DOI: https://doi.org/10.1007/s10910-018-0868-7