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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.

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Authors and Affiliations

  1. Department of Mathematics, Oriental Institute of Science and Technology, Bhopal, M.P., 462021, India

    Neha Choubey

  2. Department of Mathematics, Demonstration Multipurpose School Regional Institute of Education, Bhopal, M.P., 462013, India

    Bhavna Panday

  3. Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal, M.P., 462003, India

    J. P. Jaiswal

Authors
  1. Neha Choubey
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  2. Bhavna Panday
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  3. J. P. Jaiswal
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Correspondence to J. P. Jaiswal.

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Choubey, N., Panday, B. & Jaiswal, J.P. Several two-point with memory iterative methods for solving nonlinear equations. Afr. Mat. 29, 435–449 (2018). https://doi.org/10.1007/s13370-018-0552-x

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  • DOI: https://doi.org/10.1007/s13370-018-0552-x

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