Abstract
The complex dynamical analysis of the parametric fourth-order Kim's iterative family is made on quadratic polynomials, showing the MATLAB codes generated to draw the fractal images necessary to complete the study. The parameter spaces associated with the free critical points have been analyzed, showing the stable (and unstable) regions where the selection of the parameter will provide us the excellent schemes (or dreadful ones).
Highlights
It is usual to find nonlinear equations in the modelization of many scientific and engineering problems, and a broadly extended tools to solve them are the iterative methods
Of z0 by the rational function, The dynamical behavior of the orbit of a point on the complex plane can be classified depending on its asymptotic behavior
The main goal of drawing the dynamical and parameters planes is the comprehension of the family or method behavior at a glance
Summary
It is usual to find nonlinear equations in the modelization of many scientific and engineering problems, and a broadly extended tools to solve them are the iterative methods. Complex dynamics has been revealed as a very useful tool to deep in the understanding of the rational functions that rise when an iterative scheme is applied to solve the nonlinear equation f(z) = 0, with f : C → C. Of z0 by the rational function, The dynamical behavior of the orbit of a point on the complex plane can be classified depending on its asymptotic behavior. In this way, a point z0 ∈ C is a fixed point of R if. Point of the rational function R, its basin of attraction A(zf∗) is defined as the set of preimages of any order such that. Some conclusions and the references used in this work are presented
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