  In recent years, the first author has developed three successful numerical
methods to solve the 1D radiative transport equation yielding highly precise
benchmarks. The second author has shown a keen interest in novel solution
methodologies and an ability for their implementation. Here, we combine talents
to generate yet another high precision solution, the Matrix Riccati Equation
Method (MREM). MREM features the solution to two of the four matrix Riccati
ODEs that arise from the interaction principle of particle transport. Through
interaction coefficients, the interaction principle describes how particles
reflect from- and transmit through- a single slab. On combination with Taylor
series and doubling, a high quality numerical benchmark, to nearly seven
places, is established.
