Approximate solution of Fredholm integral equations by the maximum-entropy method

Abstract

An approximate means of solving Fredholm integral equations by the maximum-entropy method is developed. The Fredholm integral equation is converted to a generalized moment problem whose approximate solution by maximum-entropy methods has been successfully implemented in a previous paper by Mead and Papanicolaou [L. R. Mead and N. Papanicolaou, J. Math. Phys. 25, 2404 (1984)]. Several explicit examples are given of approximate maximum-entropy solutions of Fredholm integral equations of the first and second kinds and of the Wiener–Hopf type. Both the weaknesses and strengths of the method are discussed.