Comparison for accurate solutions of nonlinear Hammerstein fuzzy integral equations

Abstract

In this paper, efficient numerical techniques have been proposed to solve nonlinear Hammerstein fuzzy integral equations. The proposed methods are based on Bernsteinpolynomials and Legendre wavelets approximation. Usually, nonlinear fuzzy integral equations are very difficult to solve both analytically and numerically. The present methods applied to the integral equations is reduced to solve the system of nonlinear algebraic equations. Again, this system has been solved by Newton’s method. The numerical results obtained by present methods have been compared with those of the homotopy analysis method. Illustrative examples have been discussed to demonstrate the validity and applicability of the presented methods.