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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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Bibliographic Details
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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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
score 13.214268

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