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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Universiti Malaysia Perlis (UniMAP)
2010
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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 |
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Euler’s method Fuzzy set Fuzzy initial value Optimisation Zadeh’s extension principle Regional Conference on Applied and Engineering Mathematics (RCAEM) |
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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 |
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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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mzaini@unimap.edu.my |
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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 |
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1643789804852215808 |
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13.222552 |