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Title: A new approach to incorporate uncertainty into Euler's method
Authors: Muhammad Zaini, Ahmad
M. K., Hassan
???metadata.dc.contributor.url???: mzaini@unimap.edu.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
ISSN: 1312-885X
Appears in Collections:Institute of Engineering Mathematics (Articles)

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