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Erschienen in: Soft Computing 8/2016

28.05.2015 | Methodologies and Application

Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method

verfasst von: Omar Abu Arqub, Mohammed AL-Smadi, Shaher Momani, Tasawar Hayat

Erschienen in: Soft Computing | Ausgabe 8/2016

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Abstract

Modeling of uncertainty differential equations is very important issue in applied sciences and engineering, while the natural way to model such dynamical systems is to use fuzzy differential equations. In this paper, we present a new method for solving fuzzy differential equations based on the reproducing kernel theory under strongly generalized differentiability. The analytic and approximate solutions are given with series form in terms of their parametric form in the space \(W_2^2 [a,b]\oplus W_2^2 [a,b].\) The method used in this paper has several advantages; first, it is of global nature in terms of the solutions obtained as well as its ability to solve other mathematical, physical, and engineering problems; second, it is accurate, needs less effort to achieve the results, and is developed especially for the nonlinear cases; third, in the proposed method, it is possible to pick any point in the interval of integration and as well the approximate solutions and their derivatives will be applicable; fourth, the method does not require discretization of the variables, and it is not effected by computation round off errors and one is not faced with necessity of large computer memory and time. Results presented in this paper show potentiality, generality, and superiority of our method as compared with other well-known methods.

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Literatur
Zurück zum Zitat Abu Arqub O, Al-Smadi M, Shawagfeh N (2013a) Solving Fredholm integro-differential equations using reproducing kernel Hilbert space method. Appl Math Comput 219:8938–8948. doi:10.1016/j.amc.2013.03.006 Abu Arqub O, Al-Smadi M, Shawagfeh N (2013a) Solving Fredholm integro-differential equations using reproducing kernel Hilbert space method. Appl Math Comput 219:8938–8948. doi:10.​1016/​j.​amc.​2013.​03.​006
Zurück zum Zitat Abu Arqub O, El-Ajou A, Momani S, Shawagfeh N (2013b) Analytical solutions of fuzzy initial value problems by HAM. Appl Math Inf Sci 7:1903–1919. doi:10.12785/amis/070528 Abu Arqub O, El-Ajou A, Momani S, Shawagfeh N (2013b) Analytical solutions of fuzzy initial value problems by HAM. Appl Math Inf Sci 7:1903–1919. doi:10.​12785/​amis/​070528
Zurück zum Zitat Abu Arqub O (2015) An iterative method for solving fourth-order boundary value problems of mixed type integro-differential equations. J Comput Anal Appl 8:857–874MathSciNetMATH Abu Arqub O (2015) An iterative method for solving fourth-order boundary value problems of mixed type integro-differential equations. J Comput Anal Appl 8:857–874MathSciNetMATH
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Zurück zum Zitat Abu Arqub O, Momani S, Al-Mezel S, Kutbi M (2015) Existence, uniqueness, and characterization theorems for nonlinear fuzzy integrodifferential equations of Volterra type. Math Probl Eng. doi:10.1155/2015/835891 Abu Arqub O, Momani S, Al-Mezel S, Kutbi M (2015) Existence, uniqueness, and characterization theorems for nonlinear fuzzy integrodifferential equations of Volterra type. Math Probl Eng. doi:10.​1155/​2015/​835891
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Metadaten
Titel
Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method
verfasst von
Omar Abu Arqub
Mohammed AL-Smadi
Shaher Momani
Tasawar Hayat
Publikationsdatum
28.05.2015
Verlag
Springer Berlin Heidelberg
Erschienen in
Soft Computing / Ausgabe 8/2016
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-015-1707-4

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