example, we consider a neutron transport problem using the absorption cross section for iron at room temperature and a Watt fission spectrum for our source. Whereas opacities contain lines, nuclear cross sections for neutron applications contain resonances, which are similar to lines. The cross sections in natural iron contain thousands of fine resonances much like previous examples contained many lines.

Our final example is an atmospheric TRT calculation using $12$ homogeneous atmospheric layers from $0-15$ km, and taking a cross-section corresponding to water vapor over the frequency interval $1000\leq\nu\leq2000$ (in units of 1/cm); the cross-section for water vapor exhibits thousands of lines in this frequency range.

Let us discuss the approximation scheme first for Sections \[sub:Example-1:-the\] and \[sub:Example-2:-iron\], since the discretization schemes are essentially identical; we discuss the approximation scheme for the atmospheric problem in more detail in Section \[sub:An-atmospheric-TRT\].

We consider a transport equation of the form $$\mu\partial_{x}\psi_{\varepsilon}\left(x,\mu,E\right)+\sigma_{\varepsilon}\left(E\right)\psi_{\varepsilon}\left(x,\mu,E\right)=S\left(E\right).\label{eq:transport in slab geometry}$$ In Section \[sub:Example-1:-the\], $\sigma_{\varepsilon}\left(E\right)$ denotes the Elasser band opacity (\[eq:Elsasser band model, intro\]) and $S\left(E\right)$ denotes $\sigma_{\varepsilon}\left(E\right)B\left(E,T\right)$, with $B\left(E,T\right)$ denoting the Planck function at constant temperature; in Section \[sub:Example-2:-iron\], $\sigma_{\varepsilon}\left(E\right)$ denotes the cross-section for iron at room temperature and $S\left(E\right)$ denotes a Watts fission spectrum.

To compute the 