An ecient method, based on the Legendre wavelets, is proposed to solve thesecond kind Fredholm and Volterra integral equations of Hammerstein type.The properties of Legendre wavelet family are utilized to reduce a nonlinearintegral equation to a system of nonlinear algebraic equations, which is easilyhandled with the well-known Newton's method. Examples assuring eciencyof the method and its sup...

In this paper we intend to offer new numerical methods to solvethe fuzzy Fredholm- Volterra integral equations of the firstkind $(FVFIE-1)$. Some examples are investigated to verify convergence results and to illustrate the efficiently of the methods.  

in this paper, we will compare a homotopy perturbation algorithm and taylor series expansin method for a system of second kind fredholm integral equations. an application of he’s homotopy perturbation method is applied to solve the system of fredholm integral equations. taylor series expansin method reduce the system of integral equations to a linear system of ordinary differential equation.

This paper gives an efficient numerical method for solving the nonlinear system of Volterra-Fredholm integral equations. A Legendre-spectral method based on the Legendre integration Gauss points and Lagrange interpolation is proposed to convert the nonlinear integral equations to a nonlinear system of equations where the solution leads to the values of unknown functions at collocation points.

In this paper‎, ‎first we propose a new method to approximate the solution of two-dimensional linear fuzzy Fredholm integral equations of the second kind based on the fuzzy wavelet like operator‎. ‎Then‎, ‎we discuss and investigate the convergence and error analysis of the proposed method‎. ‎Finally‎, ‎to show the accuracy of the proposed method‎, ‎we present two numerical ‎examples.‎

in this paper, an effective direct method to determine the numerical solution of linear and nonlinear fredholm and volterra integral and integro-differential equations is proposed. the method is based on expanding the required approximate solution as the elements of chebyshev cardinal functions. the operational matrices for the integration and product of the chebyshev cardinal functions are des...

In this paper, existence theorems for the fuzzy Volterra-Fredholm integral equations of mixed type (FVFIEMT) involving fuzzy number valued mappings have been investigated. Then, by using Banach's contraction principle, sufficient conditions for the existence of a unique solution of FVFIEMT are given. Finally, illustrative examples are presented to validate the obtained results.

In this paper, a numerical method for solving fuzzy Fredholm integral equations of the second kind is introduced. We apply the trapezoidal rule to compute the Riemann integrals.This kind of integral equations convert to a linear system. Then, by solving the linear system , unknowns are determined. Finally, an algorithm is presented to solve the fuzzy integral equation by using the trapezoidal r...

Fuzzy differential and integral equations have been studied by many authors [1, 2, 5, 6, 7, 14]. Kaleva [5] discussed the properties of differentiable fuzzy set-valued mappings by means of the concept of H-differentiability introduced by Puri and Ralescu [9]. Seikkala [11] defined the fuzzy derivative which is a generalization of the Hukuhara derivative [9] and the fuzzy integral which is the s...

in this paper, we propose and analyze an efficient matrix methodbased on bell polynomials for numerically solving nonlinear fredholm- volterraintegral equations. for this aim, first we calculate operational matrix of integration and product based on bell polynomials. by using these matrices, nonlinearfredholm-volterra integral equations reduce to the system of nonlinear algebraicequations which...