Factorization of operators II: A nonlinear Volterra method for numerical solution of linear Fredholm equations

摘要

Factorization of integral operators is studied as a method for solving Fredholmequations. It is concluded that, by factorization, linear Fredholm equations can be effectively replaced by nonlinear Volterra equations. As a byproduct of the investigation, constructive proofs are obtained for existence and uniqueness of solutions to certain nonlinear systems of Volterra equations in two independent variables. Numerical examples are given.