polynomial approximations for the solution of two-dimensional linear volterra integral equations

in this paper, the residual function minimization approach is applied for the approximation of solution of two- dimensional volterra integral equations. in this method, the solution of the two- dimensional integral equations are approximated as a linear combination of polynomials. the unknown parameters of an approximate solution are obtained based on minimization of the residual function. existence and convergence of those approximate solutions are investigated. for the confirm the efficiency and accuracy of the proposed method, some numerical examples are presented.