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Newton-Kantorovich convergence theorem of a new modified Halley’s method family in a Banach space
Journal article   Open access  Peer reviewed

Newton-Kantorovich convergence theorem of a new modified Halley’s method family in a Banach space

Rongfei Lin, Yueqing Zhao, Zdeněk Šmarda, Qingbiao Wu and Yasir Khan
Advances in difference equations, Vol.2013(1), pp.325-325
19/11/2013
DOI: https://doi.org/10.1186/1687-1847-2013-325

Abstract

Analysis Boundary Value Problems Difference and Functional Equations Fixed Point Theory and Applications Functional Analysis general General Inequalities Mathematics Mathematics and Statistics Ordinary Differential Equations Partial Differential Equations Recent Advances in Operator Equations
A Newton-Kantorovich convergence theorem of a new modified Halley’s method family is established in a Banach space to solve nonlinear operator equations. We also present the main results to reveal the competence of our method. Finally, two numerical examples arising in the theory of the radiative transfer, neutron transport and in the kinetic theory of gasses are provided to show the application of our theorem.
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https://doi.org/10.1186/1687-1847-2013-325View
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