Afrika Matematika

, Volume 29, Issue 3–4, pp 435–449 | Cite as

Several two-point with memory iterative methods for solving nonlinear equations

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Abstract

In this article, our main motivation is to present two-step with memory iterative methods for solving nonlinear equations. We attempted to convert the existing fourth-order without memory method into a with memory method. Further acceleration of convergence order is attained by means of different approximations of self-accelerating parameters. The parameters are calculated by Hermite interpolating polynomial and applied to accelerate the order of convergence of the without memory methods. In particular, the R-order of the proposed two-step with memory iterative method is increased without any additional calculations and it possesses high computational efficiency. At the end, the theoretical results are confirmed by considering different numerical examples. Numerical comparisons specify that the new family is efficient and give tough competition to some existing with memory iterative methods.

Keywords

Iterative method With memory scheme Hermite interpolation polynomial Computational efficiency Numerical result 

Mathematics Subject Classification

34G20 74G15 

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Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsOriental Institute of Science and TechnologyBhopalIndia
  2. 2.Department of MathematicsDemonstration Multipurpose School Regional Institute of EducationBhopalIndia
  3. 3.Department of MathematicsMaulana Azad National Institute of TechnologyBhopalIndia

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