The response matrix discrete ordinates solution to the 1D radiative transfer equation

•Presents a new solution to the RTE called the response matrix DOM (RM/DOM).•Solution representations avoid the instability common in exponential solutions.•Explicit form in terms of matrix hyperbolic functions.•Extreme accuracy through Wynn-epsilon acceleration checked by published benchmarks.•Provides a more transparent numerical evaluation than found previously.

The discrete ordinates method (DOM) of solution to the 1D radiative transfer equation has been an effective method of solution for nearly 70 years. During that time, the method has experienced numerous improvements as numerical and computational techniques have become more powerful and efficient. Here, we again consider the analytical solution to the discrete radiative transfer equation in a homogeneous medium by proposing a new, and consistent, form of solution that improves upon previous forms. Aided by a Wynn-epsilon convergence acceleration, its numerical evaluation can achieve extreme precision as demonstrated by comparison with published benchmarks. Finally, we readily extend the solution to a heterogeneous medium through the star product formulation producing a novel benchmark for closed form Henyey-Greenstein scattering as an example.