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On developing fourth order optimal families of methods for multiple roots and their dynamics
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| Organization: | Instituto de Matem´atica Multidisciplinar, Universitat Polit`ecnica de Val`encia |
| Organization: | Instituto de Matem´atica Multidisciplinar, Universitat Polit`ecnica de Val`encia |
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| Applied Mathematics and Computation |
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There are few optimal fourth-order methods for solving nonlinear equations when the multiplicity m of the required root is known in advance. Therefore, the first focus of this paper is on developing new fourth-order optimal families of iterative methods by a simple and elegant way. Computational and theoretical properties are fully studied along with a main theorem describing the convergence analysis. Another main focus of this paper is the dynamical analysis of the rational map associated with our proposed class for multiple roots; as far as we know, there are no deep study of this kind on iterative methods for multiple roots. Further, using Mathematica with its high precision compatibility, a variety of concrete numerical experiments and relevant results are extensively treated to confirm the theoretical development.
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