Incorporating optimisation technique into Euler’s method for solving differential equations with fuzzy initial values

1st Regional Conference on Applied and Engineering Mathematics (RCAEM-I) 2010 organized by Universiti Malaysia Perlis (UniMAP) and co-organized by Universiti Sains Malaysia (USM) & Universiti Kebangsaan Malaysia (UKM), 2nd - 3rd June 2010 at Eastern & Oriental Hotel, Penang.

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Main Authors:	Muhammad Zaini, Ahmad, Mohammad Khatim, Hasan
Other Authors:	mzaini@unimap.edu.my
Format:	Working Paper
Language:	English
Published:	Universiti Malaysia Perlis (UniMAP) 2010
Subjects:	Euler’s method Fuzzy set Fuzzy initial value Optimisation Zadeh’s extension principle Regional Conference on Applied and Engineering Mathematics (RCAEM)
Online Access:	http://dspace.unimap.edu.my/xmlui/handle/123456789/10295
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Institution:	Universiti Malaysia Perlis
Language:	English

id	my.unimap-10295
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spelling	my.unimap-102952010-11-25T02:48:48Z Incorporating optimisation technique into Euler’s method for solving differential equations with fuzzy initial values Muhammad Zaini, Ahmad Mohammad Khatim, Hasan mzaini@unimap.edu.my khatim@ftsm.ukm.my Euler’s method Fuzzy set Fuzzy initial value Optimisation Zadeh’s extension principle Regional Conference on Applied and Engineering Mathematics (RCAEM) 1st Regional Conference on Applied and Engineering Mathematics (RCAEM-I) 2010 organized by Universiti Malaysia Perlis (UniMAP) and co-organized by Universiti Sains Malaysia (USM) & Universiti Kebangsaan Malaysia (UKM), 2nd - 3rd June 2010 at Eastern & Oriental Hotel, Penang. Fuzzy set provides a powerful technique to introduce uncertainty into numerical methods. However, the computations of fuzzy sets often face difficult problems. This is due to non-applicability of common existing methods, severe overestimation in computation, or very high computational complexity. This paper proposes a new strategy to introduce uncertainty into Euler’s method. It consists of two parts. First, we develop a new fuzzy version of Euler’s method, which takes into account the dependency problem that arises in the classical Euler’s method. Second, we perform optimisation technique to approximate the solution of differential equations with fuzzy initial values. This combination gives accurate results and requires only few function evaluations. Several examples are provided to show the capability of our proposed methods compared to the conventional fuzzy version of Euler’s method proposed in the literature. 2010-11-25T02:48:48Z 2010-11-25T02:48:48Z 2010-06-02 Working Paper http://hdl.handle.net/123456789/10295 en Proceedings of the 1st Regional Conference on Applied and Engineering Mathematics (RCAEM-I) 2010 Universiti Malaysia Perlis (UniMAP) Institut Matematik Kejuruteraan
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	Euler’s method Fuzzy set Fuzzy initial value Optimisation Zadeh’s extension principle Regional Conference on Applied and Engineering Mathematics (RCAEM)
spellingShingle	Euler’s method Fuzzy set Fuzzy initial value Optimisation Zadeh’s extension principle Regional Conference on Applied and Engineering Mathematics (RCAEM) Muhammad Zaini, Ahmad Mohammad Khatim, Hasan Incorporating optimisation technique into Euler’s method for solving differential equations with fuzzy initial values
description	1st Regional Conference on Applied and Engineering Mathematics (RCAEM-I) 2010 organized by Universiti Malaysia Perlis (UniMAP) and co-organized by Universiti Sains Malaysia (USM) & Universiti Kebangsaan Malaysia (UKM), 2nd - 3rd June 2010 at Eastern & Oriental Hotel, Penang.
author2	mzaini@unimap.edu.my
author_facet	mzaini@unimap.edu.my Muhammad Zaini, Ahmad Mohammad Khatim, Hasan
format	Working Paper
author	Muhammad Zaini, Ahmad Mohammad Khatim, Hasan
author_sort	Muhammad Zaini, Ahmad
title	Incorporating optimisation technique into Euler’s method for solving differential equations with fuzzy initial values
title_short	Incorporating optimisation technique into Euler’s method for solving differential equations with fuzzy initial values
title_full	Incorporating optimisation technique into Euler’s method for solving differential equations with fuzzy initial values
title_fullStr	Incorporating optimisation technique into Euler’s method for solving differential equations with fuzzy initial values
title_full_unstemmed	Incorporating optimisation technique into Euler’s method for solving differential equations with fuzzy initial values
title_sort	incorporating optimisation technique into euler’s method for solving differential equations with fuzzy initial values
publisher	Universiti Malaysia Perlis (UniMAP)
publishDate	2010
url	http://dspace.unimap.edu.my/xmlui/handle/123456789/10295
_version_	1643789804852215808

Incorporating optimisation technique into Euler’s method for solving differential equations with fuzzy initial values

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