A new approach to incorporate uncertainty into Euler's method
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2011
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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 |
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Universiti Malaysia Perlis |
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| language |
English |
| topic |
Euler’s Method Fuzzy initial value Fuzzy set Optimisation |
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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 |
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1643789906430918656 |