In this article, we give some results concerning the continuity of the nonlinear Volterra and Fredholm integral operators on the space L1[0,∞). Then by using the concept of measure of weak noncompactness, we prove an existence result for a functional integral equation which includes several classes of nonlinear integral equations. Our results extend some previous works.

In this paper, we studied the numerical solution of nonlinear weakly singular Volterra-Fredholm integral equations by using the product integration method. Also, we shall study the convergence behavior of a fully discrete version of a product integration method for numerical solution of the nonlinear Volterra-Fredholm integral equations. The reliability and efficiency of the proposed scheme are...

Since various problems in science and engineering fields can be modeled by nonlinear Volterra-Fredholm integral equations, the main focus of this study is to present an effective numerical method for solving them. This method is based on the hybrid functions of Legendre polynomials and block-pulse functions. By using this approach, a nonlinear Volterra-Fredholm integral equation reduces to a no...

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, 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.

A numerical method for solving nonlinear Fredholm-Volterra integral equations of general type is presented. This method is based on replacement of unknown function by truncated series of well known Chebyshev expansion of functions. The quadrature formulas which we use to calculate integral terms have been imated by Fast Fourier Transform (FFT). This is a grate advantage of this method which has...

Orthogonal functions and polynomials have been used by many authors for solving various problems. The main idea of using orthogonal basis is that a problem reduces to solving a system of linear or nonlinear algebraic equations by truncated series of orthogonal basis functions for solution of problem and using the operational matrices. Here we use Legendre wavelets basis on interval [0, 1]. Some...

In this paper the method of integral equations is proposed for some problems of electrical engineering ( current density, radiative heat transfer, heat conduction). Presented models lead to a system of Fredholm integral equations, integro-differential equations or Volterra-Fredholm integral equations, respectively. We propose various numerical methods (discretization method and projection metho...

Here, the solution in one, two and three dimensional for the Volterra–Fredholm integral equation of the first kind is obtained in the space L2ðXÞ C1⁄20; T , T < 1. Using a numerical method the integral equation of Volterra–Fredholm becomes a linear system of Fredholm integral equation when that the kernel of Fredholm integral takes a logarithmic form, Carleman function, generalized potential fu...