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Appl. Syst. Innov. 2018, 1(2), 15; https://doi.org/10.3390/asi1020015

New Fuzzy Numerical Methods for Solving Cauchy Problems

1
Institute of Engineering Mathematics, Universiti Malaysia Perlis, Kampus Tetap Pauh Putra, Arau 02600, Perlis, Malaysia
2
Institute for Research and Applications of Fuzzy Modelling, University of Ostrava, NSC IT4Innovations, 30. dubna 22, 701 03 Ostrava, Czech Republic
*
Author to whom correspondence should be addressed.
Received: 7 April 2018 / Revised: 1 May 2018 / Accepted: 3 May 2018 / Published: 11 May 2018
(This article belongs to the Special Issue Fuzzy Decision Making and Soft Computing Applications)
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Abstract

In this paper, new fuzzy numerical methods based on the fuzzy transform (F-transform or FT) for solving the Cauchy problem are introduced and discussed. In accordance with existing methods such as trapezoidal rule, Adams Moulton methods are improved using FT. We propose three new fuzzy methods where the technique of FT is combined with one-step, two-step, and three-step numerical methods. Moreover, the FT with respect to generalized uniform fuzzy partition is able to reduce error. Thus, new representations formulas for generalized uniform fuzzy partition of FT are introduced. As an application, all these schemes are used to solve Cauchy problems. Further, the error analysis of the new fuzzy methods is discussed. Finally, numerical examples are presented to illustrate these methods and compared with the existing methods. It is observed that the new fuzzy numerical methods yield more accurate results than the existing methods. View Full-Text
Keywords: fuzzy partition; fuzzy transform; new iterative method; Cauchy problems fuzzy partition; fuzzy transform; new iterative method; Cauchy problems
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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ALKasasbeh, H.; Perfilieva, I.; Ahmad, M.Z.; Yahya, Z.R. New Fuzzy Numerical Methods for Solving Cauchy Problems. Appl. Syst. Innov. 2018, 1, 15.

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