A full fuzzy method for solving differential equation based on Taylor expansion

Issue title: Dedicated to Professor Lotfi A. Zadeh and Fifty Years of Fuzzy Logic

Article type: Research Article

Authors: Allahviranloo, T.^{a; b; *} | Gouyandeh, Z.^a | Armand, A.^a

Affiliations: [a] Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran | [b] Department of Mathematics and Statistics, University of Prince Edward Island, 550 University Ave, Charlottetown, Canada

Correspondence: [*] Corresponding author. T. Allahviranloo. Tel.: +989123508816; Fax: +982144865030; E-mail: [email protected].

Abstract: In this paper, the fuzzy Taylor expansion is presented based on the concept of generalized Hukuhara differentiability. Using the fuzzy Taylor expansion, the Euler method and its local and global truncation errors are defined for solving fuzzy initial value problems. Moreover, the consistency, convergence and stability of the Euler method are provided in details. Finally, for illustration some numerical examples are solved.

Keywords: Generalized Hukuhara derivative, fuzzy Taylor expansion, fuzzy Euler method, global truncation error, local truncation error

DOI: 10.3233/IFS-151713

Journal: Journal of Intelligent & Fuzzy Systems, vol. 29, no. 3, pp. 1039-1055, 2015