Fuzzy Fredholm Integral Equations Research Articles

Error estimation in the approximation of the solution of nonlinear fuzzy Fredholm integral equations

Using a fixed point technique, the sequence of successive approximations and a recent quadrature formula for fuzzy-number-valued functions, it is constructed a numerical method for the solution of nonlinear fuzzy Fredholm integral equations. Moreover, the error estimate of the method and a criterion to stop the corresponding algorithm are given.

Numerical method for solving linear Fredholm fuzzy integral equations of the second kind

In this paper we use parametric form of fuzzy number and convert a linear fuzzy Fredholm integral equation to two linear system of integral equation of the second kind in crisp case. We can use one of the numerical method such as Nystrom and find the approximation solution of the system and hence obtain an approximation for fuzzy solution of the linear fuzzy Fredholm integral equations of the second kind. The proposed method is illustrated by solving some numerical examples.

Numerical solution of linear Fredholm fuzzy integral equations of the second kind by Adomian method

Using parametric form of fuzzy numbers we convert a linear fuzzy Fredholm integral equation of the second kind to a linear system of integral equations of the second kind in crisp case. We use Adomian method and find the approximate solution of this system and hence obtain an approximation for fuzzy solution of the linear fuzzy Fredholm integral equation of the second kind. We apply the method to some examples.

Solutions to fuzzy integral equations with arbitrary kernels

Using a parametric Riemann integral representation, a numerical algorithm for solving fuzzy Fredholm and Voltera integral equations of the second kind with arbitrary kernel is proposed and illustrated with examples.

On Fuzzy Integral Equations

Using the embedding method, the fuzzy integral is represented as a parametric Riemann integral. An algorithm which approximates this integral uniformly, is incorporated to design a soft computing tool for solving a fuzzy Fredholm integral equation of the second kind with arbitrary kernel, using a uniformly convergent iterative procedure.