‎The subject of this paper is the solution of the Fredholm integral equation with Toeplitz, Hankel and the Toeplitz plus Hankel kernel. The mean value theorem for integrals is applied and then extended for solving high dimensional problems and finally, some example and graph of error function are presented to show the ability and simplicity of the ‎method.

In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra-Fredholm integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using this matrices, the nonlinear two-dimensional Vol...

In this paper, we propose a numerical method based on the generalized hat functions (GHFs) and improved hat functions (IHFs) to find numerical solutions for stochastic Volterra-Fredholm integral equation. To do so, all known and unknown functions are expanded in terms of basic functions and replaced in the original equation. The operational matrices of both basic functions are calculated and em...

In this paper, an effective numerical method is introduced for the treatment of nonlinear two-dimensional Volterra-Fredholm integro-differential equations. Here, we use the so-called two-dimensional block-pulse functions.First, the two-dimensional block-pulse operational matrix of integration and differentiation has been presented. Then, by using this matrices, the nonlinear two-dimensional Vol...

urysohn integral equation is one of the most applicable topics in both pure and applied mathematics. the main objective of this paper is to solve the urysohn type fredholm integral equation. to do this, we approximate the solution of the problem by substituting a suitable truncated series of the well known legendre polynomials instead of the known function. after discretization of the problem o...

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...

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.

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...

T The nonlinear and linear Volterra-Fredholm ordinary integral equations arise from various physical and biological models. The essential features of these models are of wide applicable. These models provide an important tool for modeling a numerous problems in engineering and science [6, 7]. Modelling of certain physical phenomena and engineering problems [8, 9, 10, 11, 12] leads to two-dimens...