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Analytical and numerical solutions of fuzzy differential equations

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Main Authors: Muhammad Zaini, Ahmad, Dr., Mohammad Khatim, Hasan, Assoc. Prof. Dr., De Baets, Bernard
Other Authors: mzaini@unimap.edu.my
Format: Article
Language:English
Published: Elsevier Inc. 2014
Subjects:
Dependency problem
Fuzzy derivative
Fuzzy differential equation
Numerical method
Online Access:http://dspace.unimap.edu.my:80/dspace/handle/123456789/32479
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spelling my.unimap-324792014-03-10T05:04:41Z Analytical and numerical solutions of fuzzy differential equations Muhammad Zaini, Ahmad, Dr. Mohammad Khatim, Hasan, Assoc. Prof. Dr. De Baets, Bernard mzaini@unimap.edu.my khatim@ftsm.ukm.my Dependency problem Fuzzy derivative Fuzzy differential equation Numerical method Link to publisher's homepage at http://www.elsevier.com/ In this paper, we study analytical and numerical solutions of fuzzy differential equations based on the extension principle. For linear fuzzy differential equations, we state some results on the behaviour of the solutions and study their relationship with the generalised Hukuhara derivative. In order to approximate the solutions of linear and non-linear fuzzy differential equations, we propose a new fuzzification of the classical Euler method and then incorporate an unconstrained optimisation technique. This combination offers a powerful tool to tackle uncertainty in any numerical method. An efficient computational algorithm is also provided to guarantee the convexity of fuzzy solutions on the time domain. Several illustrative examples are given. 2014-03-10T05:04:41Z 2014-03-10T05:04:41Z 2013-07 Article Information Sciences, vol. 236, 2013, pages 156-167 0020-0255 http://www.sciencedirect.com/science/article/pii/S0020025513001436 http://dspace.unimap.edu.my:80/dspace/handle/123456789/32479 en Elsevier Inc.
institution Universiti Malaysia Perlis
building UniMAP Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaysia Perlis
content_source UniMAP Library Digital Repository
url_provider http://dspace.unimap.edu.my/
language English
topic Dependency problem
Fuzzy derivative
Fuzzy differential equation
Numerical method
spellingShingle Dependency problem
Fuzzy derivative
Fuzzy differential equation
Numerical method
Muhammad Zaini, Ahmad, Dr.
Mohammad Khatim, Hasan, Assoc. Prof. Dr.
De Baets, Bernard
Analytical and numerical solutions of fuzzy differential equations
description Link to publisher's homepage at http://www.elsevier.com/
author2 mzaini@unimap.edu.my
author_facet mzaini@unimap.edu.my
Muhammad Zaini, Ahmad, Dr.
Mohammad Khatim, Hasan, Assoc. Prof. Dr.
De Baets, Bernard
format Article
author Muhammad Zaini, Ahmad, Dr.
Mohammad Khatim, Hasan, Assoc. Prof. Dr.
De Baets, Bernard
author_sort Muhammad Zaini, Ahmad, Dr.
title Analytical and numerical solutions of fuzzy differential equations
title_short Analytical and numerical solutions of fuzzy differential equations
title_full Analytical and numerical solutions of fuzzy differential equations
title_fullStr Analytical and numerical solutions of fuzzy differential equations
title_full_unstemmed Analytical and numerical solutions of fuzzy differential equations
title_sort analytical and numerical solutions of fuzzy differential equations
publisher Elsevier Inc.
publishDate 2014
url http://dspace.unimap.edu.my:80/dspace/handle/123456789/32479
_version_ 1643796912188424192
score 13.222552

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