About an artificial time approach for iterative numerical solution of Fredholm integral equations of the first kind

An iterative method exploiting artificial time iteration is presented and applied to the solution of Fredholm integral equations of the first kind, discretized by a collocation method based on Variation Diminishing Schoenberg (VDS) spline approximations. Convergence theorem of iterative method is provided. The presented iterative method is also used to solve known problems discretized by both classical Galerkin and quadrature methods. More, the choice of the linear discrete regularization operator is discussed within the context of Tikhonov regularization. Numerical results are reported to show the effectiveness of the presented approach.