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Developing high order methods for the solution of systems of nonlinear equations

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  • Chun, Changbum
  • Neta, Beny

Abstract

Two families of order six for the solution of systems of nonlinear equations are developed and compared to existing schemes of order up to six. We have found that one of the methods in the literature has been rediscovered. The comparison is based on the total cost of an iteration and the performance on 14 examples of systems of dimensions 2–9.

Suggested Citation

  • Chun, Changbum & Neta, Beny, 2019. "Developing high order methods for the solution of systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 178-190.
    • Handle: RePEc:eee:apmaco:v:342:y:2019:i:c:p:178-190
    DOI: 10.1016/j.amc.2018.09.032
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    References listed on IDEAS

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    1. Abbasbandy, Saeid & Bakhtiari, Parisa & Cordero, Alicia & Torregrosa, Juan R. & Lotfi, Taher, 2016. "New efficient methods for solving nonlinear systems of equations with arbitrary even order," Applied Mathematics and Computation, Elsevier, vol. 287, pages 94-103.
    2. Artidiello, S. & Cordero, Alicia & Torregrosa, Juan R. & Vassileva, M.P., 2017. "Design and multidimensional extension of iterative methods for solving nonlinear problems," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 194-203.
    3. Sharma, Janak Raj & Sharma, Rajni & Kalra, Nitin, 2015. "A novel family of composite Newton–Traub methods for solving systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 520-535.
    4. H. Montazeri & F. Soleymani & S. Shateyi & S. S. Motsa, 2012. "On a New Method for Computing the Numerical Solution of Systems of Nonlinear Equations," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-15, November.
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    Cited by:

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    2. Zhanlav, T. & Otgondorj, Kh., 2021. "Higher order Jarratt-like iterations for solving systems of nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 395(C).

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