An analytical version of the discrete ordinates method is used to solve a class of boundary-value problems based on a linear Boltzmann equation relevant to the transport of neutral hydrogen atoms in a hydrogen plasma. In addition to a complete development of the discrete ordinates method for the considered application, the computational algorithm is implemented to yield very accurate results for a number of half-space and finite-slab problems. The developed code is also used to correct some entries in a previously reported tabulation of results. The established algorithm is considered especially easy to use, and the code runs (typically) in <1 s on a 400-MHz Pentium-based personal computer.