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Neural Computing and Applications

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15.12.2015 | Original Article

Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations

verfasst von: Omar Abu Arqub

Erschienen in: Neural Computing and Applications | Ausgabe 7/2017

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Abstract

In this article, we propose the reproducing kernel Hilbert space method to obtain the exact and the numerical solutions of fuzzy Fredholm–Volterra integrodifferential equations. The solution methodology is based on generating the orthogonal basis from the obtained kernel functions in which the constraint initial condition is satisfied, while the orthonormal basis is constructing in order to formulate and utilize the solutions with series form in terms of their r-cut representation form in the Hilbert space \( W_{2}^{2} \left( \varOmega \right) \oplus W_{2}^{2} \left( \varOmega \right) \). Several computational experiments are given to show the good performance and potentiality of the proposed procedure. Finally, the utilized results show that the present method and simulated annealing provide a good scheduling methodology to solve such fuzzy equations.

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Titel: Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations
verfasst von: Omar Abu Arqub
Publikationsdatum: 15.12.2015
Verlag: Springer London
Erschienen in: Neural Computing and Applications / Ausgabe 7/2017
Print ISSN: 0941-0643
Elektronische ISSN: 1433-3058
DOI: https://doi.org/10.1007/s00521-015-2110-x

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