Mathematics and Natural Sciences
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 2, 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.
Journal of Computational and Applied Mathematics
(2016). Solving Fredholm Integral Equations via a Piecewise Linear Maximum Entropy Method. Journal of Computational and Applied Mathematics, 304, 130-137.
Available at: https://aquila.usm.edu/fac_pubs/15347