Abstract
A new parametric family of iterative schemes for solving nonlinear systems is presented. Fourth-order convergence is demonstrated and its stability is analyzed as a function of the parameter values. This study allows us to detect the most stable elements of the class, to find the fractals in the boundary of the basins of attraction and to reject those with chaotic behavior. Some numerical tests show the performance of the new methods, confirm the theoretical results and allow to compare the proposed schemes with other known ones.
Funder
Ministerio de Ciencia, Innovación y Universidades
Subject
Statistics and Probability,Statistical and Nonlinear Physics,Analysis
Cited by
6 articles.
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