Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems

In this paper, we investigate the analytic and approximate solutions of second-order, two-point fuzzy boundary value problems based on the reproducing kernel theory under the assumption of strongly generalized differentiability. The solution methodology is based on generating the orthogonal basis fr...

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Vydané v:Soft computing (Berlin, Germany) Ročník 21; číslo 23; s. 7191 - 7206
Hlavní autori: Arqub, Omar Abu, Al-Smadi, Mohammed, Momani, Shaher, Hayat, Tasawar
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2017
Springer Nature B.V
Predmet:
Algorithms
Artificial Intelligence
Boundary value problems
Computational Intelligence
Computational mathematics
Control
Engineering
Kernel functions
Mathematical Logic and Foundations
Mechatronics
Methodologies and Application
Numerical analysis
Ordinary differential equations
Robotics
Fuzzy boundary value problems
Gram–Schmidt process
Strongly generalized differentiability
Reproducing kernel theory
ISSN:1432-7643, 1433-7479
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Shrnutí:In this paper, we investigate the analytic and approximate solutions of second-order, two-point fuzzy boundary value problems based on the reproducing kernel theory under the assumption of strongly generalized differentiability. The solution methodology is based on generating the orthogonal basis from the obtained kernel functions, while the orthonormal basis is constructing in order to formulate and utilize the solutions with series form in terms of their r -cut representation in the space ⊕ j = 1 2 W 2 3 a , b . An efficient computational algorithm is provided to guarantee the procedure and to confirm the performance of the proposed method. Results of numerical experiments are provided to illustrate the theoretical statements in order to show potentiality, generality, and superiority of our algorithm for solving such fuzzy equations. Graphical results, tabulated data, and numerical comparisons are presented and discussed quantitatively to illustrate the possible fuzzy solutions.
Bibliografia:ObjectType-Article-1
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ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-016-2262-3