Numerical Solution for Solving System of Fuzzy Nonlinear Integral Equation by Using Modified Decomposition Method

Alan Jalal Abdulqader

doi:10.5539/jmr.v10n1p32

Abstract

In this paper, we intend to offer system of fuzzy nonlinear integral equation also numerical scheme to solve. by using the new and fast technique to solve our problem. we try to discuss some numerical aspects such as convergence and error analysis. Finally, accuracy and applicability of the proposed methods are carried out along with comparisons using some numerical examples.

Highlights

1.IntroductionFuzzy systems are used to study a various of problems ranging from fuzzy metric spaces
In recent years, Fuzzy systems are used to study a various of problems ranging from fuzzy metric spaces
Yalcinbas (Babolian, E., Biazar, J. & Vahidi, A.R., 2004), as two of the most important basic polynomials which in previous works have not been covered in fuzzy equations,Modified decomposition method is proposed to solve complexity composition fuzzy kernels and complexity fuzzy nonlinear integral equation with complexly kernels, we convert a fuzzy nonlinear integral equation to a system of integral equation some numerical examples are presented to show the facts about our methods

Summary

1.Introduction

Fuzzy systems are used to study a various of problems ranging from fuzzy metric spaces The concept of integration of fuzzy functions was _firstly introduced by Dubois and Prade (1982). A fuzzy number ǔ in parametric form is a pair (u, u)of function u(α), u(α), 0 ≤ α ≤ 1, which satisfies the following requiremenst: i) u(α) is a bounded left continuous non- decreasing function over [0, 1] ii) u(α) is a bounded left continuous non- increasing function over [0, 1] iii) u(α) ≤ u(α), 0 ≤ α ≤ 1 Definition 2.6, If the fuzzy function f(t) is continuous in metric D,its definite the integral exists and (∫ab f(t; α)dt ) =∫ab f (t; α)dt,. ∫ce kmj(x, t, Gmj (t, F (t, ujm(t, α))) dt+∫ex kmj(x, t, Gmj (t, F (t, ujm(t, α))) dt] This is the condition for the fuzzy nonlinear integral system. We will explain modified decomposition method to solve our system and find the approximate solution for ũ(x) a ≤ x ≤ b

Modified Decomposition Method

Conclusion