Three Step Kurchatov Method for Nondifferentiable Operators

Abstract

In this paper we find the order of convergence and semilocal convergence of three step Kurchatov-type method. We also analyze the efficiency index and computational efficiency of this method. The semilocal convergence analysis of method has been established by using recurrence relations under the assumption of first order divided difference operators satisfy Lipschitz condition. The convergence theorem and domain of parameters of the method has also been included. The applicability of the proposed convergence analysis is illustrated by solving some numerical examples.

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Correspondence to P. K. Parida.

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Kumar, H., Parida, P.K. Three Step Kurchatov Method for Nondifferentiable Operators. Int. J. Appl. Comput. Math 3, 3683–3704 (2017). https://doi.org/10.1007/s40819-017-0321-9

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Keywords

  • Nonlinear equations
  • Order of convergence
  • Kurchatov’s method
  • Efficiency index
  • Computational efficiency
  • Recurrence relations
  • Semilocal convergence

Mathematics Subject Classfication

  • 47H99
  • 65H10