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Efficient High-Order Iterative Methods for Solving Nonlinear Systems and Their Application on Heat Conduction Problems

Author

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  • Alicia Cordero
  • Esther Gómez
  • Juan R. Torregrosa

Abstract

For solving nonlinear systems of big size, such as those obtained by applying finite differences for approximating the solution of diffusion problem and heat conduction equations, three-step iterative methods with eighth-order local convergence are presented. The computational efficiency of the new methods is compared with those of some known ones, obtaining good conclusions, due to the particular structure of the iterative expression of the proposed methods. Numerical comparisons are made with the same existing methods, on standard nonlinear systems and a nonlinear one-dimensional heat conduction equation by transforming it in a nonlinear system by using finite differences. From these numerical examples, we confirm the theoretical results and show the performance of the presented schemes.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:complx:6457532
    DOI: 10.1155/2017/6457532
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    Cited by:

    1. Abro, Hameer Akhtar & Shaikh, Muhammad Mujtaba, 2019. "A new time-efficient and convergent nonlinear solver," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 516-536.
    2. Deepak Kumar & Ioannis K. Argyros & Janak Raj Sharma, 2018. "Convergence Ball and Complex Geometry of an Iteration Function of Higher Order," Mathematics, MDPI, vol. 7(1), pages 1-13, December.
    3. 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.

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