Solving Fredholm integral equations via a piecewise linear maximum entropy method

We propose a piecewise linear approximation method, based on the maximum entropy principle, to approximate a nonnegative solution of a Fredholm integral equation numerically. The theoretical analysis and numerical examples show that our method has a convergence rate of order 22, and it can get more accurate approximations with more moments used without ill-condition of the classic maximum entropy approach. The method can also be applied to solve Fredholm integral equations with singular kernels.