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F-transform-based shooting method for nonlinear boundary value problems

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Abstract

We study a class of ordinary two-point boundary value problems for nonlinear second-order ordinary differential equations. We propose to use the framework of shooting method and apply the second-degree F-transform for solving the corresponding initial value problem. We make experiments that demonstrate effectiveness of the proposed F-transform-based shooting method in the class of second-order numerical methods. Moreover, we show stability of the proposed method and its ability to “ignore noise”.

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Notes

  1. The text of this and the following subsection is a free version of a certain part of Perfilieva et al. (2011) where the theory of a higher-degree F-transform was introduced.

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Acknowledgements

This work has been supported by the Project “LQ1602 IT4Innovations excellence in science” and by the Grant Agency of the Czech Republic (Project No. 16-09541S).

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Authors and Affiliations

  1. Centre of Excellence IT4Innovations, Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. dubna 22, Ostrava, Czech Republic

    Irina Perfilieva, Petra Števuliáková & Radek Valášek

Authors
  1. Irina Perfilieva
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  2. Petra Števuliáková
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  3. Radek Valášek
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Correspondence to Irina Perfilieva.

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This article does not contain any studies with human participants or animals performed by any of the authors.

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Communicated by F. Di Martino, V. Novákc.

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Perfilieva, I., Števuliáková, P. & Valášek, R. F-transform-based shooting method for nonlinear boundary value problems. Soft Comput 21, 3493–3502 (2017). https://doi.org/10.1007/s00500-017-2543-5

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  • DOI: https://doi.org/10.1007/s00500-017-2543-5

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