Stability study of eighth-order iterative methods for solving nonlinear equations

Alicia Cordero ^[1] ; Alberto Magreñán ^[2] ; Carlos Quemada ^[3] ; Juan R. Torregrosa ^[1]
1. [1] Universidad Politécnica de Valencia
  
  Universidad Politécnica de Valencia
  
  Valencia, España
2. [2] Universidad Internacional de La Rioja
  
  Universidad Internacional de La Rioja
  
  Logroño, España
3. [3] Virginia University, USA
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Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 291, Nº 1 (1 January 2016), 2016, págs. 348-357
Idioma: inglés
DOI: 10.1016/j.cam.2015.01.006
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Resumen
- In this paper, we study the stability of the rational function associated to a known family of eighth-order iterative schemes on quadratic polynomials. The asymptotic behavior of the fixed points corresponding to the rational function is analyzed and the parameter space is shown, in which we find choices of the parameter for which there exists convergence to cycles or even chaotical behavior showing the complexity of the family. Moreover, some elements of the family with good stability properties are obtained.