In this work, we consider two-dimensional linear and nonlinear Fredholm integral equations of the first kind. The combination of the regularization method and the homotopy perturbation method, or shortly, the regularization-homotopy method is used to find a solution to the equation. The application of this method is based upon converting the first kind of equation to the second kind by applying...

In this paper, a new approach to determine the numerical solution of two-dimensional fuzzy Fredholm integral equation of the second kind (2DFFIE2) is proposed. This method is based on the fuzzy bivariate Bernstein polynomials. By using fuzzy bivariate Bernstein polynomials, a 2DFFIE2 can be transformed to a dual fuzzy linear system. The error estimate of this method is presented in terms of the...

The Karhunen-Loève expansion of a Gaussian process, a common tool on finite element methods for differential equations with stochastic coefficients, is based on the spectral decomposition of its covariance function. The eigenpairs of the covariance are expressed as a Fredholm integral equation of second kind, which can be readily approximated with piecewise-constant finite elements. In this wor...

This paper presents a numerical method for solving the stochastic nonlinear volterra-fredholm integral equation (SNVFIE) driven by a standard Brownian motion (SBM). The method is illustrated via a stochastic operational matrix (SOM) based on the triangular functions (TFs) in combination with the collocation method. With using this approach, the SNVFIE reduces to a stochastic nonlinear system of...

The two-dimensional problem of advection–dispersion associated with a non-aqueousphase liquid (NAPL) pool is addressed using the boundary element method. The problem is appropriately posed with an inhomogeneous boundary condition taking into consideration the presence of the pool and the impermeable layer. We derive a Fredholm integral equation of the first kind for the concentration gradient a...

We derive and analyze two equivalent integral formulations for the time-harmonic electromagnetic scattering by a dielectric object. One is a volume integral equation (VIE) with a strongly singular kernel and the other one is a coupled surface-volume system of integral equations with weakly singular kernels. The analysis of the coupled system is based on standard Fredholm integral equations, and...

In this paper, a nonlinear Volterra-Fredholm integral equation of the first kind is solved by using the homotopy analysis method (HAM). In this case, the first kind integral equation can be reduced to the second kind integral equation which can be solved by HAM. The approximate solution of this equation is calculated in the form of a series which its components are computed easily. The accuracy...

recently, the block-pulse functions (bpfs) are used in solving electromagnetic scattering problem, which are modeled as linear fredholm integral equations (fies) of the second kind. but the theoretical aspect of this method has not fully investigated yet. in this article, in addition to presenting a new approach for solving fie of the second kind, the theory of both methods is investigated as a...

in this paper, he‘s variational iteration method is applied to fredholm integral equations of the second kind. to illustrate the ability and simplicity of the method, some examples are provided. the results reveal that the proposed method is very effective and simple and for first fourth examples leads to the exact solution.