On efficient two‐parameter methods for solving nonlinear equations

On efficient two‐parameter methods for solving nonlinear equations

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Article ID: iaor20134206
Volume: 63
Issue: 3
Start Page Number: 549
End Page Number: 569
Publication Date: Jul 2013
Journal: Numerical Algorithms
Authors:
Keywords: interpolation
Abstract:

Derivative free methods for solving nonlinear equations of Steffensen’s type are presented. Using two self‐correcting parameters, calculated by Newton’s interpolatory polynomials of second and third degree, the order of convergence is increased from 2 to 3.56. This method is used as a corrector for a family of biparametric two‐step derivative free methods with and without memory with the accelerated convergence rate up to order 7. Significant acceleration of convergence is attained without any additional function calculations, which provides very high computational efficiency of the proposed methods. Another advantage is a convenient fact that the proposed methods do not use derivatives. Numerical examples are given to demonstrate excellent convergence behavior of the proposed methods and good coincidence with theoretical results.

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