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Generalized High-Order Classes for Solving Nonlinear Systems and Their Applications

Author

Listed:
  • Francisco I. Chicharro

    (Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, 26006 Logroño, Spain
    These authors contributed equally to this work.)

  • Alicia Cordero

    (Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain
    These authors contributed equally to this work.)

  • Neus Garrido

    (Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, 26006 Logroño, Spain
    These authors contributed equally to this work.)

  • Juan R. Torregrosa

    (Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain
    These authors contributed equally to this work.)

Abstract

A generalized high-order class for approximating the solution of nonlinear systems of equations is introduced. First, from a fourth-order iterative family for solving nonlinear equations, we propose an extension to nonlinear systems of equations holding the same order of convergence but replacing the Jacobian by a divided difference in the weight functions for systems. The proposed GH family of methods is designed from this fourth-order family using both the composition and the weight functions technique. The resulting family has order of convergence 9. The performance of a particular iterative method of both families is analyzed for solving different test systems and also for the Fisher’s problem, showing the good performance of the new methods.

Suggested Citation

  • Francisco I. Chicharro & Alicia Cordero & Neus Garrido & Juan R. Torregrosa, 2019. "Generalized High-Order Classes for Solving Nonlinear Systems and Their Applications," Mathematics, MDPI, vol. 7(12), pages 1-14, December.
  • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1194-:d:294666
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    References listed on IDEAS

    as
    1. Alicia Cordero & Esther Gómez & Juan R. Torregrosa, 2017. "Efficient High-Order Iterative Methods for Solving Nonlinear Systems and Their Application on Heat Conduction Problems," Complexity, Hindawi, vol. 2017, pages 1-11, January.
    2. Amiri, Abdolreza & Cordero, Alicia & Taghi Darvishi, M. & Torregrosa, Juan R., 2018. "Stability analysis of a parametric family of seventh-order iterative methods for solving nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 43-57.
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