Semilocal convergence of a modified multi-point Jarratt method in Banach spaces under general continuity condition

Authors:
Xiuhua Wang;Jisheng Kou
Affiliations:
School of Mathematics and Statistics, Xiaogan University, Xiaogan, China 432100;School of Mathematics and Statistics, Xiaogan University, Xiaogan, China 432100
Venue:
Numerical Algorithms
Year:
2012

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Abstract

The semilocal convergence for a modified multi-point Jarratt method for solving non-linear equations in Banach spaces is established with the third-order Fréchet derivative of the operator under a general continuity condition. The recurrence relations are derived for the method, and from this, we prove an existence-uniqueness theorem, and give a priori error bounds. The R-order of the method is also analyzed with the third-order Fréchet derivative of the operator under different continuity conditions. Numerical application on non-linear integral equation of the mixed type is given to show our approach.