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A new approach to incorporate uncertainty into Euler's method

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Bibliographic Details
Main Authors: Muhammad Zaini, Ahmad, M. K., Hassan
Other Authors: mzaini@unimap.edu.my
Format: Article
Language:English
Published: Hikari Ltd 2011
Subjects:
Euler’s Method
Fuzzy initial value
Fuzzy set
Optimisation
Online Access:http://dspace.unimap.edu.my/xmlui/handle/123456789/10449
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spelling my.unimap-104492011-01-10T02:55:52Z A new approach to incorporate uncertainty into Euler's method Muhammad Zaini, Ahmad M. K., Hassan mzaini@unimap.edu.my khatim@ftsm.ukm.my Euler’s Method Fuzzy initial value Fuzzy set Optimisation Link to publisher's homepage at http://www.m-hikari.com/ 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 propose 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 turns out to be a great tool to tackle uncertainty in any numerical method. One example is provided to show the capability of our proposed methods compared to the conventional fuzzy version of Euler’s method proposed in the literature. 2011-01-10T02:55:52Z 2011-01-10T02:55:52Z 2010 Article Applied Mathematical Sciences, vol. 4(49-52), 2010, pages 2509-2520 1312-885X http://www.m-hikari.com/ams/ams-2010/ams-49-52-2010/ahmadAMS49-52-2010.pdf http://hdl.handle.net/123456789/10449 en Hikari Ltd
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 initial value
Fuzzy set
Optimisation
spellingShingle Euler’s Method
Fuzzy initial value
Fuzzy set
Optimisation
Muhammad Zaini, Ahmad
M. K., Hassan
A new approach to incorporate uncertainty into Euler's method
description Link to publisher's homepage at http://www.m-hikari.com/
author2 mzaini@unimap.edu.my
author_facet mzaini@unimap.edu.my
Muhammad Zaini, Ahmad
M. K., Hassan
format Article
author Muhammad Zaini, Ahmad
M. K., Hassan
author_sort Muhammad Zaini, Ahmad
title A new approach to incorporate uncertainty into Euler's method
title_short A new approach to incorporate uncertainty into Euler's method
title_full A new approach to incorporate uncertainty into Euler's method
title_fullStr A new approach to incorporate uncertainty into Euler's method
title_full_unstemmed A new approach to incorporate uncertainty into Euler's method
title_sort new approach to incorporate uncertainty into euler's method
publisher Hikari Ltd
publishDate 2011
url http://dspace.unimap.edu.my/xmlui/handle/123456789/10449
_version_ 1643789906430918656
score 13.211869

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