Semilocal convergence of a sixth-order method in Banach spaces

Authors:
Lin Zheng;Chuanqing Gu
Affiliations:
Department of Mathematics, Shanghai University, Shanghai, China 200444;Department of Mathematics, Shanghai University, Shanghai, China 200444
Venue:
Numerical Algorithms
Year:
2012

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Abstract

In this paper, we introduce a new iterative method of order six and study the semilocal convergence of the method by using the recurrence relations for solving nonlinear equations in Banach spaces. We prove an existence-uniqueness theorem and give a priori error bounds which demonstrates the R-order of the method to be six. Finally, we give some numerical applications to demonstrate our approach.