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Multidimensional Homeier’s generalized class and its application to planar 1D Bratu problem

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Abstract

In this paper, a parametric family of iterative methods for solving nonlinear systems, including Homeier’s scheme is presented, proving its third-order of convergence. The numerical section is devoted to obtain an estimation of the solution of the classical Bratu problem by transforming it in a nonlinear system by using finite differences, and solving it with different elements of the iterative family.

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Authors and Affiliations

  1. Instituto Universitario de Matematica Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022, Valencia, Spain

    Alicia Cordero, Antonio Franques & Juan R. Torregrosa

Authors
  1. Alicia Cordero
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  2. Antonio Franques
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  3. Juan R. Torregrosa
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Corresponding author

Correspondence to Juan R. Torregrosa.

Additional information

This research was supported by Ministerio de Economía y Competitividad MTM2014-52016-C02-02.

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Cordero, A., Franques, A. & Torregrosa, J.R. Multidimensional Homeier’s generalized class and its application to planar 1D Bratu problem. SeMA 70, 1–10 (2015). https://doi.org/10.1007/s40324-015-0037-x

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  • DOI: https://doi.org/10.1007/s40324-015-0037-x

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