A Third Order Newton-Like Method and Its Applications

D. R. Sahu, Ravi P. Agarwal and Vipin Kumar Singh
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D. R. Sahu: Department of Mathematics, Banaras Hindu University, Varanasi-221005, India
Ravi P. Agarwal: Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363-8202, USA
Vipin Kumar Singh: Department of Mathematics, Banaras Hindu University, Varanasi-221005, India

Mathematics, 2018, vol. 7, issue 1, 1-22

Abstract: In this paper, we design a new third order Newton-like method and establish its convergence theory for finding the approximate solutions of nonlinear operator equations in the setting of Banach spaces. First, we discuss the convergence analysis of our third order Newton-like method under the ω -continuity condition. Then we apply our approach to solve nonlinear fixed point problems and Fredholm integral equations, where the first derivative of an involved operator does not necessarily satisfy the Hölder and Lipschitz continuity conditions. Several numerical examples are given, which compare the applicability of our convergence theory with the ones in the literature.

Keywords: nonlinear operator equation; Fréchet derivative; ?-continuity condition; Newton-like method; Frédholm integral equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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