The Solution of Fredholm Integral Equations of Second Kind by Ritz Approach

A new constructive method to solve Fredholm integral equations of second kind is proposed. This method is based on an analytical procedure that recursively generates a sequence of functions uN, N ∈N. Under suitable conditions, this sequence converges to the solution u∗ of the integral equation under consideration. Several practical versions of this procedure can be obtained by considering different approximation schemes. In particular, following the Ritz approach, the various functions arisen from the analytical method are rewritten by considering a suitable orthogonal system. So that, from the analytical method, we obtain an algorithm for the computation of the coefficients of uN with respect to the orthogonal system taken into account