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A class of two-point sixth-order multiple-zero finders of modified double-Newton type and their dynamics.
- Source :
-
Applied Mathematics & Computation . Nov2015, Vol. 270, p387-400. 14p. - Publication Year :
- 2015
-
Abstract
- Under the assumption of the known multiplicity of zeros of nonlinear equations, a class of two-point sextic-order multiple-zero finders and their dynamics are investigated in this paper by means of extensive analysis of modified double-Newton type of methods. With the introduction of a bivariate weight function dependent on function-to-function and derivative-to-derivative ratios, higher-order convergence is obtained. Additional investigation is carried out for extraneous fixed points of the iterative maps associated with the proposed methods along with a comparison with typically selected cases. Through a variety of test equations, numerical experiments strongly support the theory developed in this paper. In addition, relevant dynamics of the proposed methods is successfully explored for various polynomials with a number of illustrative basins of attraction. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00963003
- Volume :
- 270
- Database :
- Academic Search Index
- Journal :
- Applied Mathematics & Computation
- Publication Type :
- Academic Journal
- Accession number :
- 110308874
- Full Text :
- https://doi.org/10.1016/j.amc.2015.08.039