A proposal for the calculation of characteristic functions for certain differential and integral operators via initial-value methods

AbstractThis paper presents an initial-value method for the solution of the inhomogeneous Fredholm integral equation u(t) = g(t) + λ ∝0c k(¦ t − y ¦) u(y) dy. These equations and an expansion formula of classical analysis allow a proposal to be made for calculating the solutions to the homogeneous equation φ(t) = λ ∝0c k(¦ t − y ¦) φ(y) dy.The paper discusses possible numerical difficulties and presents extensions to other types of linear operators