Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/67630
Type: Artigo
Title: On fuzzy solutions for partial differential equations
Author: Betone, Ana Maria
Jafelice, Rosana Motta
Barros, Laécio Carvalho
Bassanezi, Rodney Carlos
Abstract: In this study we investigate heat, wave and Poisson equations as classical models of partial differential equations (PDEs) with uncertain parameters, considering the parameters as fuzzy numbers. The fuzzy solution is built from fuzzification of the deterministic solution. The continuity of the Zadeh extension is used to obtain qualitative properties on regular alpha-cuts of the fuzzy solution. We prove the stability with respect to the initial boundary data, and show that as time goes to zero, the diameter of the fuzzy solution converges to zero and, as a consequence, to the cylindrical surface determined by the curve of the degree of membership. Numerical simulations are used to obtain a graphical representation of the fuzzy solution and a defuzzification of this solution is obtained using the center of gravity method. We theoretically show that the surface obtained by defuzzification with the plane determined by fixing time is indeed the solution of the same initial boundary problem for this time-point for the heat and Poisson equations and, in a particular case, for the wave equation. The deterministic solution and the defuzzified surface intercept are numerically compared using the Euclidean distance. (C) 2013 Elsevier B.V. All rights reserved.
In this study we investigate heat, wave and Poisson equations as classical models of partial differential equations (PDEs) with uncertain parameters, considering the parameters as fuzzy numbers. The fuzzy solution is built from fuzzification of the determ
Subject: Números fuzzy
Equações diferenciais parciais
Country: Países Baixos
Editor: Elsevier
Citation: Fuzzy Sets And Systems. Elsevier Science Bv, v. 219, n. 68, n. 80, 2013.
Rights: Fechado
Identifier DOI: 10.1016/j.fss.2012.12.002
Address: https://www.sciencedirect.com/science/article/pii/S0165011412005040
Date Issue: 2013
Appears in Collections:IMECC - Artigos e Outros Documentos

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