Semilocal convergence of a sixth-order Jarratt method in Banach spaces

Authors:
Xiuhua Wang;Jisheng Kou;Chuanqing Gu
Affiliations:
Department of Mathematics, Shanghai University, Shanghai, People's Republic of China 200444 and Department of Mathematics, Xiaogan University, Xiaogan, People's Republic of China 432100;Department of Mathematics, Shanghai University, Shanghai, People's Republic of China 200444;Department of Mathematics, Shanghai University, Shanghai, People's Republic of China 200444
Venue:
Numerical Algorithms
Year:
2011

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Abstract

In this paper, we study the semilocal convergence for a sixth-order variant of the Jarratt method for solving nonlinear equations in Banach spaces. The semilocal convergence of this method is established by using recurrence relations. We derive the recurrence relations for the method, and then prove an existence-uniqueness theorem, along with a priori error bounds which demonstrates the R-order of the method. Finally, we give some numerical applications to demonstrate our approach.