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Modifying Kurchatov's method to find multiple roots of nonlinear equations
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  • Juan Ramon Torregrosa,
  • Alicia Cordero,
  • Neus Garrido,
  • Paula Triguero-Navarro
Juan Ramon Torregrosa
Universitat Politecnica de Valencia

Corresponding Author:jrtorre@mat.upv.es

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Alicia Cordero
Universitat Politecnica de Valencia
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Neus Garrido
Universitat Politecnica de Valencia
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Paula Triguero-Navarro
Universitat Politecnica de Valencia
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Abstract

In this work, we modify the iterative Kurchatov's method to solve nonlinear equations with multiple roots, that is,for approximating the solutions of multiplicity grater than one. Its main feature is that you do not need to know a priori the multiplicity of the root, which does not appear in the iterative expression. We perform a dynamical analysis to see the behaviour of the proposed method. We also carry out some numerical experiments to confirm the theoretical results and compare the proposed method with other known schemes for multiple roots.