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

Author(s)

Wasques, Vinicius Francisco

• Document type: Journal article
• Source: COMPUTATIONAL & APPLIED MATHEMATICS; v. 43, n. 6, p. 13-pg., 2024-09-01.

Abstract

This paper presents a numerical approach to solve fuzzy partial differential equation restrictto fuzzy boundary and initial conditions. The numerical solution to this problem is obtainedby the finite difference method considering a particular type of fuzzy arithmetic calledJ0-interactive arithmetic. A study of the computational cost of the method is presented, as wellas a comparison with the numerical solution obtained by the standard fuzzy arithmetic, whichis associated with the Zadeh's extension principle. The paper focuses on the heat equation inorder to illustrate the methodology. (AU)

• FAPESP's process: 23/03927-0 - Fuzzy differential equations and fuzzy algebra with applications
• Grantee: Vinícius Francisco Wasques
• Support Opportunities: Regular Research Grants