Recurrence relations for semilocal convergence of a fifth-order method in Banach spaces |
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Authors: | Lin Zheng Chuanqing Gu |
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Institution: | 1.Department of Mathematics,Shanghai University,Shanghai,China |
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Abstract: | In this paper, we study the semilocal convergence for a fifth-order method for solving nonlinear equations in Banach spaces.
The semilocal convergence of this method is established by using recurrence relations. We prove an existence-uniqueness theorem
and give a priori error bounds which demonstrates the R-order of the method. As compared with the Jarratt method in Hernández
and Salanova (Southwest J Pure Appl Math 1:29–40, 1999) and the Multi-super-Halley method in Wang et al. (Numer Algorithms 56:497–516, 2011), the differentiability conditions of the convergence of the method in this paper are mild and the R-order is improved. Finally,
we give some numerical applications to demonstrate our approach. |
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