A methodology for solving the one-dimensional mono-energetic transport equation in homogeneous semi-infinite medium

摘要

In this paper, we implement and verify an algorithm based on the eigendecomposition method to solve the one-dimensional mono-energetic transport equation in a semi-infinite medium with isotropic scattering. Using our algorithm, we produce approximate closed-form expressions for the solution. Moreover, the algorithm does not utilize a Laplace transform, offers reasonable accuracy, and displays rapid convergence using a relatively small number of quadrature points.