The use of fuzzy expansion method for solving fuzzy linear Volterra-Fredholm integral equations

Article type: Research Article

Authors: Behzadi, Sh.S. | Allahviranloo, T. | Abbasbandy, S.

Affiliations: Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

Note: [] Corresponding author. Sh.S. Behzadi, Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran. E-mails: shadan_behzadi@yahoo.com; tofigh@allahviranloo.com (T. Allahviranloo); abbasbandy@yahoo.com (S. Abbasbandy).

Abstract: In this paper, the fuzzy Fast Galerkin method (FFGM) and the fuzzy collocation method (FCM) have been used to solve the fuzzy linear Volterra-Fredholm integral equation of the second kind (FVFIE – 2). We convert a fuzzy linear Volterra-Fredholm integral equation to a system of fuzzy equations by using FFGM and FCM. The existence and uniqueness of the solution and convergence of the proposed method are proved in detail. Finally some examples show the accuracy of these methods.

Keywords: Fuzzy number, Volterra-Fredholm integral equations, Fuzzy Galerkin method, Fuzzy collocation method

DOI: 10.3233/IFS-130861

Journal: Journal of Intelligent & Fuzzy Systems, vol. 26, no. 4, pp. 1817-1822, 2014