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. 2 5, 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.