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A New Three-Step Class of Iterative Methods for Solving Nonlinear Systems

Author

Listed:
  • Raudys R. Capdevila

    (Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain
    Dpto. de Educación en Línea, Universidad San Francisco de Quito, Quito 170901, Ecuador)

  • Alicia Cordero

    (Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain)

  • Juan R. Torregrosa

    (Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain)

Abstract

In this work, a new class of iterative methods for solving nonlinear equations is presented and also its extension for nonlinear systems of equations. This family is developed by using a scalar and matrix weight function procedure, respectively, getting sixth-order of convergence in both cases. Several numerical examples are given to illustrate the efficiency and performance of the proposed methods.

Suggested Citation

  • Raudys R. Capdevila & Alicia Cordero & Juan R. Torregrosa, 2019. "A New Three-Step Class of Iterative Methods for Solving Nonlinear Systems," Mathematics, MDPI, vol. 7(12), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1221-:d:296469
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    References listed on IDEAS

    as
    1. Artidiello, Santiago & Cordero, Alicia & Torregrosa, Juan R. & Vassileva, Maria P., 2015. "Multidimensional generalization of iterative methods for solving nonlinear problems by means of weight-function procedure," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1064-1071.
    2. F. Soleymani & M. Sharifi & S. Shateyi & F. Khaksar Haghani, 2014. "A Class of Steffensen-Type Iterative Methods for Nonlinear Systems," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-9, April.
    3. Candela, V. & Peris, R., 2019. "A class of third order iterative Kurchatov–Steffensen (derivative free) methods for solving nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 93-104.
    4. 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.
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