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Please use this identifier to cite or link to this item:
http://hdl.handle.net/123456789/10449
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| Title: | A new approach to incorporate uncertainty into Euler's method |
| Authors: | Muhammad Zaini, Ahmad
M. K., Hassan |
| E-mail: | mzaini@unimap.edu.my
khatim@ftsm.ukm.my |
| Keywords: | Euler’s Method
Fuzzy initial value
Fuzzy set
Optimisation |
| Issue Date: | 2010 |
| Publisher: | Hikari Ltd |
| Citation: | Applied Mathematical Sciences, vol. 4(49-52), 2010, pages 2509-2520 |
| Abstract: | 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. |
| Description: | Link to publisher's homepage at http://www.m-hikari.com/ |
| URI: | http://www.m-hikari.com/ams/ams-2010/ams-49-52-2010/ahmadAMS49-52-2010.pdf
http://hdl.handle.net/123456789/10449 |
| ISSN: | 1312-885X |
| Appears in Collections: | Institut Matematik Kejuruteraan (Articles)
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