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

Advances in Difference Equations

Zdenk marda¹  Yueqing Zhao²  Rongfei Lin²  Yasir Khan³  Qingbiao Wu³ 

[1] Department of Mathematics, Brno University of Technology, Brno, Czech Republic;Department of Mathematics, Taizhou University, Linhai, P.R. China;Department of Mathematics, Zhejiang University, Hangzhou, P.R. China

关键词: Banach Space;    Iterative Method;    Radiative Transfer;    Positive Root;    Positive Real Root;   

DOI  :  10.1186/1687-1847-2013-325

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY