numerical solution of fuzzy integral equation

What is it about?

In this paper, first, we introduce method of successive approximations in terms of midpoint quadrature formula, which is given for solving linear fuzzy Fredholm integral equations (FFIEs) of the second kind. Moreover, the convergence of the proposed method is given. Also we investigate the numerical stability of the proposed method with respect to the choice of the first iteration. Finally, two numerical examples are presented to show the accuracy of the proposed method.

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Why is it important?

Due to the the error bound of midpoint rule in comparing Trapezoidal and Simpson rules, and also according to the fact that Trapezoidal and Simpson rules can not be used for approximate integrals which they are not dened in rst and end points of integration , in these article we used the approximate solution of the fuzzy integral equation by using midpoint rule and compare it with these methods.