On developing a novel sixth order transformation method for multiple roots and its basins of attraction

• Rajni Sharma ^[2] ; Ashu Bahl ^[1]
  1. [1] Punjab Technical University

     Punjab Technical University

     India

     
  2. [2] Institute of Engineering and Technology
• Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 76, Nº. 4, 2019, págs. 595-613
• Idioma: inglés
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• Resumen

  • In this contribution, a novel sixth-order transformation method is proposed and analyzed for finding multiple roots of nonlinear equations, when the multiplicity of the root is not known explicitly. The proposed method does not require the evaluation of second derivative. Numerical examples are presented to demonstrate the robust and efficient behavior of the proposed scheme. The basins of attraction of the proposed method are also presented in comparison to existing transformation methods in the literature.