Abstract
A generalized k-step iterative method from Steffensen’s method with frozen divided difference operator for solving a system of nonlinear equations is studied and the maximum computational efficiency is computed. Moreover, a sequence that approximates the order of convergence is generated for the examples and it confirms in a numerical way that the order of the method and the computational efficiency are both well deduced. By using a technique based on recurrence relations, the semilocal convergence of the family is studied. Finally, some numerical experiments related to the approximation of nonlinear elliptic equations are reported. A comparison with other derivative-free families of iterative methods is carried out.
Funding statement: This work was supported in part by the project MTM2011-28636-C02-01 of the Spanish Ministry of Science and Innovation. Research supported in part by Programa de Apoyo a la investigación de la fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia 19374/PI/14 and MTM2015-64382-P (MINECO/FEDER).
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