Pointwise Bivariational Bounds on Solutions of Fredholm Integral Equations

Abstract

Pointwise bounds of a bivariational nature are derived on the solution of a standard Fredholm integral equation of the second kind, with a symmetric kernel. The bounding functionals involve, two trial vectors, one approximating the solution and the other approximating the reciprocal kernel. Even with the latter taken as the null vector, there is significant improvement over a previous approach. In an illustrative example, five-figure accuracy is achieved with one-parameter functions. It is shown how suitable choices of trial vector lead to expressions for bounds on Neumann, Padé and Fredholm approximations.