Application of ‎F‎uzzy Bicubic Splines Interpolation for Solving ‎T‎wo-Dimensional Linear Fuzzy Fredholm Integral ‎Equations‎‎

Subject Areas : International Journal of Industrial Mathematics

H.  ‎Nouriani‎ ¹ (Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.)
R.  ‎Ezzati‎‎‎ ² (Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.)

Received: 2009-09-25 Accepted : 2019-02-16 Published : 2019-04-01

Keywords: Fuzzy‎ ‎numbers‎, Iterative method, Two dimensional fuzzy splines‎ ‎interpolation, Two-dimensional linear fuzzy‎ ‎Fredholm integral equations,

Abstract :

‎In this paper‎, ‎firstly‎, ‎we review approximation of fuzzy functions‎ ‎by fuzzy bicubic splines interpolation and present a new approach‎ ‎based on the two-dimensional fuzzy splines interpolation and‎ ‎iterative method to approximate the solution of two-dimensional‎ ‎linear fuzzy Fredholm integral equation (2DLFFIE)‎. ‎Also‎, ‎we prove‎ ‎convergence analysis and numerical stability analysis for the‎ ‎proposed numerical algorithm‎. ‎Finally‎, ‎by an example‎, ‎we show the‎ ‎efficiency of the proposed ‎method.‎