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

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 const...

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Vydáno v:Neural computing & applications Ročník 28; číslo 7; s. 1591 - 1610
Hlavní autor: Abu Arqub, Omar
Médium: Journal Article
Jazyk:angličtina
Vydáno: London Springer London 01.07.2017
Springer Nature B.V
Témata:
Adaptation
Artificial Intelligence
Computational Biology/Bioinformatics
Computational Science and Engineering
Computer Science
Computer simulation
Data Mining and Knowledge Discovery
Hilbert space
Image Processing and Computer Vision
Kernel functions
Original Article
Probability and Statistics in Computer Science
Scheduling
Simulated annealing
Volterra integral equations
Gram–Schmidt process
Reproducing kernel Hilbert space method
34K28
47B32
Fuzzy integrodifferential equations
46S40
Strongly generalized differentiability
ISSN:0941-0643, 1433-3058
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Popis
Shrnutí: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 Ω ⊕ W 2 2 Ω . 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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ISSN:0941-0643
1433-3058
DOI:10.1007/s00521-015-2110-x