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Multidimensional Real Dynamics for High-Order Processes

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Finite Difference Methods. Theory and Applications (FDM 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11386))

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Abstract

In this manuscript, we design a parametric family of iterative methods for solving nonlinear problems, that does not need to evaluate Jacobian matrices and needs to solve three linear systems per iteration with the same divided difference operator as coefficient matrix. The stability performance of the class is analyzed on a quadratic polynomial system and it is shown that for a wide set of values (including positive ones), there exist only convergence to the roots of the problem.

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References

  1. Cordero, A., Gutiérrez, J.M., Magrenán, Á.A., Torregrosa, J.R.: Stability analysis of a parametric family of iterative methods for solving nonlinear models. Appl. Math. Comput. 285, 26–40 (2016)

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  2. Cordero, A., Soleymani, F., Torregrosa, J.R.: Dynamical analysis of iterative methods for nonlinear systems or how to deal with the dimension? Appl. Math. Comput. 244, 398–412 (2014)

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  3. Robinson, R.C.: An Introduction to Dynamical Systems, Continous and Discrete. Americal Mathematical Society, Providence (2012)

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  4. Chicharro, F.I., Cordero, A., Torregrosa, J.R.: Drawing dynamical and parameters planes of iterative families and methods. Sci. World J. 2013, 11 (2013). Article ID 780153

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Acknowledgement

This research was partially supported by Ministerio de Economia y Competitividad under grants MTM2014-52016-C2-2-P, Generalitat Valenciana PROMETEO/2016/089 and FONDOCYT, Dominican Republic.

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Authors and Affiliations

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

    Alicia Cordero & Juan R. Torregrosa

  2. Instituto Tecnológico de Santo Domingo, Avda. Los Próceres 49, Santo Domingo, Dominican Republic

    Javier G. Maimó & Maria P. Vassileva

Authors
  1. Alicia Cordero
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  2. Javier G. Maimó
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  3. Juan R. Torregrosa
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  4. Maria P. Vassileva
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Corresponding author

Correspondence to Alicia Cordero .

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Editors and Affiliations

  1. IICT, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. University of Rousse, Rousse, Bulgaria

    Lubin Vulkov

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Cordero, A., Maimó, J.G., Torregrosa, J.R., Vassileva, M.P. (2019). Multidimensional Real Dynamics for High-Order Processes. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods. Theory and Applications. FDM 2018. Lecture Notes in Computer Science(), vol 11386. Springer, Cham. https://doi.org/10.1007/978-3-030-11539-5_21

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  • DOI: https://doi.org/10.1007/978-3-030-11539-5_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-11538-8

  • Online ISBN: 978-3-030-11539-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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