in this paper, the two-dimensional triangular orthogonal functions (2d-tfs) are applied for solving a class of nonlinear two-dimensional volterra integral equations. 2d-tfs method transforms these integral equations into a system of linear algebraic equations. the high accuracy of this method is verified through a numerical example and comparison of the results with the other numerical methods.

in this article the nonlinear mixed volterra-fredholm integral equations are investigated by means of the modied three-dimensional block-pulse functions (m3d-bfs). this method converts the nonlinear mixed volterra-fredholm integral equations into a nonlinear system of algebraic equations. the illustrative   examples are provided to demonstrate the applicability and simplicity of our   scheme.

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, a method for finding an approximate solution of a class of two-dimensional nonlinear volterra integral equations of the first-kind is proposed. this problem is transformedto a nonlinear two-dimensional volterra integral equation of the second-kind. the properties ofthe bivariate shifted legendre functions are presented. the operational matrices of integrationtogether with the produ...

in this paper we apply the technique of measures of noncompactness to the theory of infinite system of integral equations in the fr´echet spaces. our aim is to provide a few generalization of tychonoff fixed point theorem and prove the existence of solutions for infinite systems of nonlinear integral equations with help of the technique of measures of noncompactness and a generalization of tych...

in this paper, an effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (rbfs). we present an algorithm based on interpolation by radial basis functions including multiquadratics (mqs), using legendre-gauss-lobatto nodes and weights. also a theorem is proved for convergence of the algorithm. some numerical examples are presented...

in this article, a numerical method based on  improvement of block-pulse functions (ibpfs) is discussed for solving the system of linear volterra and fredholm integral equations. by using ibpfs and their operational matrix of integration, such systems can be reduced to a linear system of algebraic equations. an efficient error estimation and associated theorems for the proposed method are also ...

Algebraic integral equations is a special category of Volterra integral equations system,  that has many applications in physics and engineering. The principal aim of this paper is to serve the numerical solution of an integral algebraic equation by using the Taylor expansion method. In this method, using the Taylor expansion of the unknown function, the algebraic integral equation system becom...