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Soft Computing
Published in: Soft Computing 13/2017

22-03-2017 | Focus

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

Authors: Irina Perfilieva, Petra Števuliáková, Radek Valášek

Published in: Soft Computing | Issue 13/2017

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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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Footnotes
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.
 
Literature
Arnold VI (1992) Ordinary differential equations. Springer, New York
Atkinson KE (1988) An introduction to numerical analysis, 2nd edn. Wiley, Iowa
Chen W, Schen Y (2014) Approximate solution for a class of second-order ordinary differencital equations by the fuzzy transform. Intell Fuzzy Syst 27:73–82
Khastan A, Perfilieva I, Alijani Z (2016) A new fuzzy approximation method to Cauchy problems by fuzzy transform. Fuzzy Sets Syst 288:75–95MathSciNetCrossRef
Khastan A, Alijani Z, Perfilieva I (2016) Fuzzy transform to approximate solution of two-point boundary value problems. Math Methods Appl Sci. doi:10.​1002/​mma.​3832
Perfilieva I (2003) Fuzzy logic in geology. In: Demicco RV, Klir GJ (eds) Fuzzy transform: application to the Reef growth problem, chap. 9. Academic Press, Amsterdam, pp 275–300
Perfilieva I, Daňková M, Bede B (2011) Towards F-transform of a higher degree. Fuzzy Sets Syst 180:3–19CrossRefMATH
Perfilieva I, Števuliáková P, Valášek R (2017) F-transform for numerical solution of two-point boundary value problem. Iran J Fuzzy Syst (accepted)
Metadata
Title
F-transform-based shooting method for nonlinear boundary value problems
Authors
Irina Perfilieva
Petra Števuliáková
Radek Valášek
Publication date
22-03-2017
Publisher
Springer Berlin Heidelberg
Published in
Soft Computing / Issue 13/2017
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-017-2543-5

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