A numerical approach to fuzzy partial differential equations with interactive fuzzy values: application to the heat equation

This paper presents a numerical approach to solve fuzzy partial differential equation restrict to fuzzy boundary and initial conditions. The numerical solution to this problem is obtained by the finite difference method considering a particular type of fuzzy arithmetic called J0-interactive arithmetic. A study of the computational cost of the method is presented, as well as a comparison with the numerical solution obtained by the standard fuzzy arithmetic, which is associated with the Zadeh’s extension principle. The paper focuses on the heat equation in order to illustrate the methodology.

Palavras-chave

34K36 Fuzzy functional differential equations, 35R13 Fuzzy partial differential equations, Fuzzy Interactivity, Fuzzy partial differential equations, Heat equation, Sup-J extension principle