In this paper, a numerical method is proposed for solving the fuzzy linear Fredholm integral equations of the second kind. For this result, we choose Legendre polynomials as basis functions and collocation method to estimate a solution for an unknown function in these equations. Finally, a numerical example will be stated to illustrate this method.

integral equations have many applications in the theory of elasticity, engineering, mathematical physics, potential theory, electrostatic and radiative heat transfer problems. In this paper, we present a method for solving fuzzy linear Fredholm integral equations of the second kind, namely “homotopy analysis method” (HAM). It is found that the HAM provides us with a simple way to adjust and control the convergence region of solution series by introducing convergence-control parameter h, which is the main advantage of this method.

In this paper,  rstly, we review approximation of fuzzy functions by fuzzy bicubic splines interpo-lation 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 equa-tion (2DLFFIE). Also, we prove convergence analysis and numerical stability analysis for the proposed numerical algorithm. Finally, by an example, we show the e ciency of the proposed method.

fuzzy integral equations play major roles in various areas, therefore a new method for finding a solution of the Fredholm fuzzy integral equation is presented. This method converts the fuzzy integral equation into linear system by using the Taylor series. For this scope, first the Taylor expansion of unknown function is substituted in parametric form of the given equation. Then we differentiate both sides of the resulting integral equation and also approximate the Taylor expansion by a suitable truncation limit. This work yields a linear system in crisp case. Now the solution of this system yields unknown Taylor coefficients of the solution functions. The proposed method is illustrated by several examples with computer simulations.

In this study, a new application of Taylor expansion is considered to estimate the solution of Volterra-Fredholm integral equations (VFIEs) and systems of Volterra-Fredholm integral equations (SVFIEs). Our proposed method is based upon utilizing the nth-order Taylor polynomial of unknown function at an arbitrary point and employing integration method to convert VFIEs into a system of linear equations with respect to unknown function and its derivatives. An approximate solution can be easily determined by solving the obtained system. Furthermore, this method leads always to the exact solution if the exact solution is a polynomial function of degree up to n. Also, an error analysis is given. In addition, some problems are provided to demonstrate the validity and applicability of the proposed method.

In this paper Homotopy Perturbation Method (HPM) to solve fuzzy Fredholm integral equations is proposed. The method is discussed in details and it is illustrated by solving some numerical examples.

In this paper a linear fuzzy Fredholm integral Equation (FFIE) with arbitrary fuzzy Function input and symmetric triangular (fuzzy Interval) output is considered. For each variable, output is the nearest triangular fuzzy number (fuzzy interval) to the exact fuzzy solution of (FFIE).