Error estimation and numerical solution of nonlinear fuzzy Fredholm integral equations of the second kind using triangular functions

Article type: Research Article

Authors: Baghmisheh, Mahdi^a | Ezzati, Reza^{b; *}

Affiliations: [a] Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran | [b] Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

Correspondence: [*] Corresponding author. Reza Ezzati, Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran. Tel.: +98 9123618518; Fax: +98 2634182300; E-mail: [email protected].

Abstract: In this paper we present an efficient iterative procedure based on the triangular functions (TFs) to obtain the numerical solution of the specific nonlinear fuzzy Fredholm integral equations of the second kind. The error estimation of the proposed method is given in terms of uniform modulus of continuity. Also, we prove the stability of the method with respect to the choice of the first iteration. Finally, in order to demonstrate the accuracy and the convergence of the method, some numerical examples are included.

Keywords: Nonlinear fuzzy Fredholm integral equation, iterative procedure, triangular functions, numerical stability

DOI: 10.3233/IFS-151783

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 639-649, 2016