Multipoint Fractional Iterative Methods with (2 ? + 1)th-Order of Convergence for Solving Nonlinear Problems

Giro Candelario, Alicia Cordero and Juan R. Torregrosa
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Giro Candelario: Área de Ciencias Básicas y Ambientales, Instituto Tecnológico de Santo Domingo (INTEC), Santo Domingo 10602, Dominican Republic
Alicia Cordero: Institute for Multidisciplinary Mathematics, Universitat Politècnica de Valenència, Camino de Vera s/n, 46022 València, Spain
Juan R. Torregrosa: Institute for Multidisciplinary Mathematics, Universitat Politècnica de Valenència, Camino de Vera s/n, 46022 València, Spain

Mathematics, 2020, vol. 8, issue 3, 1-15

Abstract: In the recent literature, some fractional one-point Newton-type methods have been proposed in order to find roots of nonlinear equations using fractional derivatives. In this paper, we introduce a new fractional Newton-type method with order of convergence α + 1 and compare it with the existing fractional Newton method with order 2 α . Moreover, we also introduce a multipoint fractional Traub-type method with order 2 α + 1 and compare its performance with that of its first step. Some numerical tests and analysis of the dependence on the initial estimations are made for each case, including a comparison with classical Newton ( α = 1 of the first step of the class) and classical Traub’s scheme ( α = 1 of fractional proposed multipoint method). In this comparison, some cases are found where classical Newton and Traub’s methods do not converge and the proposed methods do, among other advantages.

Keywords: nonlinear equations; fractional derivatives; multistep methods; convergence; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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