In this paper a numerical technique is presented for the solution of fuzzy linear Volterra-Fredholm-Hammerstein integral equations. This method is a combination of collocation method and radial basis functions(RBFs).We first solve the actual set are equivalent to the fuzzy set, then answer 1-cut into the equation. Also high convergence rates and good accuracy are obtain with the propose method ...

Degenerate kernel approximation method is generalized to solve Hammerstein system of Fredholm integral equations of the second kind. This method approximates the system of integral equations by constructing degenerate kernel approximations and then the problem is reduced to the solution of a system of algebraic equations. Convergence analysis is investigated and on some test problems, the propo...

in this paper we investigate the existence and uniqueness for volterra-fredholm type integral equations and extension of this type of integral equations. the result is obtained by using the  coupled fixed point theorems in the framework of banach space $ x=c([a,b],mathbb{r})$. finally, we  give an example to illustrate the applications of our results.

Iterative processes are a powerful tool for providing numerical methods integral equations of the second kind. Integral with symmetric kernels extensively used to model problems, e.g., optimization, electronic and optic problems. We analyze iterative Fredholm–Hammerstein modified argument. The approximation consists two parts, fixed point result quadrature formula. derive method that uses Picar...

Rationalized Haar functions are developed to approximate the solution of the nonlinear Volterra–Fredholm–Hammerstein integral equations. The properties of rationalized Haar functions are first presented. These properties together with the Newton–Cotes nodes and Newton–Cotes integration method are then utilized to reduce the solution of Volterra–Fredholm–Hammerstein integral equations to the sol...

Abstract: In this paper, a Sinc-collocation method based on the double exponential transformation for solving Fredholm and Volterra Hammerstein integral equations is presented. Some properties of the Sinc-collocation method required for our subsequent development are given and utilized to reduce the computation of solution of the Hammerstein integral equations to some algebraic equations. Numer...

The aim of this paper is solving nonlinear Volterra-Fredholm fractional integro-differential equations with mixed boundary conditions‎. ‎The basic idea is to convert fractional integro-differential equation to a type of second kind Fredholm integral equation‎. ‎Then the obtained Fredholm integral equation will be solved with Nystr"{o}m and Newton-Kantorovitch method‎.  ‎Numerical tests for demo...

Let H be a real Hilbert space. Let K, F : H → H be bounded, continuous and monotone mappings. Suppose that u∗ ∈ H is a solution to Hammerstein equation u + KFu = 0. We introduce a new explicit iterative sequence and prove strong convergence of the sequence to a solution of the Hammerstein equation.