  We describe a new, faster implicit algorithm for solving the radiation
hydrodynamics equations in the flux-limited diffusion approximation for
smoothed particle hydrodynamics. This improves on the method elucidated in
Whitehouse & Bate by using a Gauss-Seidel iterative method rather than
iterating over the exchange of energy between pairs of particles. The new
algorithm is typically many thousands of times faster than the old one, which
will enable more complex problems to be solved. The new algorithm is tested
using the same tests performed by Turner & Stone for ZEUS-2D, and repeated by
Whitehouse & Bate.
