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New efficient derivative free family of seventh-order methods for solving systems of nonlinear equations

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Abstract

We present a three-step two-parameter family of derivative free methods with seventh-order of convergence for solving systems of nonlinear equations numerically. The proposed methods require evaluation of two central divided differences and inversion of only one matrix per iteration. As a result, the proposed family is more efficient as compared with the existing methods of same order. Numerical examples show that the proposed methods produce approximations of greater accuracy and remarkably reduce the computational time for solving systems of nonlinear equations.

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Authors and Affiliations

  1. DAV College, Sector 10, Chandigarh, 160010, India

    Mona Narang

  2. University Institute of Engineering and Technology, Panjab University, Chandigarh, 160 014, India

    Saurabh Bhatia & Vinay Kanwar

Authors
  1. Mona Narang
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  2. Saurabh Bhatia
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  3. Vinay Kanwar
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Correspondence to Vinay Kanwar.

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Narang, M., Bhatia, S. & Kanwar, V. New efficient derivative free family of seventh-order methods for solving systems of nonlinear equations. Numer Algor 76, 283–307 (2017). https://doi.org/10.1007/s11075-016-0254-0

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  • DOI: https://doi.org/10.1007/s11075-016-0254-0

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