Design and extension of higher-Order derivative-free iterative methods for nonlinear systems
DOI:
https://doi.org/10.5564/mmj.v26i1.5098Keywords:
Best derivative-free iterations, Extensions of iterations, High efficiency, high-order convergence, Nonlinear systemAbstract
In this paper, we propose derivative-free two- and three-step iterative methods with easy implementation. Moreover, we suggest suitable parameter choices that guarantee a local convergence order ρ from four to eight. They require only one matrix inversion at each iteration step and belong to the class of best iterations with high efficiency indices. Several of the proposed algorithms are multidimensional extensions of well-known scalar iterative methods. Numerical experiments are presented to verify the theoretical orders of convergence and to demonstrate the computational efficiency of the proposed methods.
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