The use of Sherman-Morrison formula in the solution of Fredholm integral equation of second kind
A constructive method for the solution of Fredholm integral equations of the second kind is provided. This method is based on a simple generalization of the Sherman-Morrison formula for matrices to corresponding operators in infinite-dimensional spaces. In particular, this method is recursive and delivers a sequence of functions converging to the exact solution of the integral equation. The convergence result is proved for the case of Fredholm integral equations with square integrable kernels. The results are applied to a boundary value problem for the Laplace operator. Several variants of the employed method are suggested.
Fredholm integral equation of second kind
scientific article; zbMATH DE number 5843137
scientific article