Analytical and numerical solutions of fuzzy differential equations
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2014
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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. |
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Malaysia |
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Universiti Malaysia Perlis |
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| language |
English |
| topic |
Dependency problem Fuzzy derivative Fuzzy differential equation Numerical method |
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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 |