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...

The topic of the Adomian decomposition method has been rapidly growing in recent years. The concept of this method was first introduced by G. Adomian in the beginning of 1980’s [1, 2]. In this method the solution of a functional equations is considered as the sum of an infinite series usually converging to the solution [3]. The Adomian decomposition method for solving linear and nonlinear integ...

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...

the density and polarization profiles of the dipolar hard ellipsoids confined between hard walls are studied using the density functional theory (dft). the hyper-netted chain (hnc) approximation is used to write excess grand potential of the system with respect to the bulk value. the number density is expanded up to zero and first order in polarization to find the results. for the zero order in...

We illustrate several adaptive algorithms for the solutions of bi-infinite singular linear systems. Such algorithms are realized from exact iterative schemes (e.g., Richardson, steepest-descent methods, matching pursuit) by finite dimensional approximations of each iteration, performed with a greedy approach. We show that these algorithms are convergent and optimal with respect to certain spars...

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...

The density and polarization profiles of the dipolar hard ellipsoids confined between hard walls are studied using the density functional theory (DFT). The Hyper-Netted Chain (HNC) approximation is used to write excess grand potential of the system with respect to the bulk value. The number density is expanded up to zero and first order in polarization to find the results. For the zero order in...

This paper describes an approximating solution, based on Lagrange interpolation and spline functions, to treat functional integral equations of Fredholm type and Volterra type. This method can be extended to functional differential and integro-differential equations. For showing efficiency of the method we give some numerical examples.

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 ...