We have written the implicit adaptive grid code {\TITAN} which solves the comoving-frame
equations of Newtonian radiation hydrodynamics in one spatial dimension. This code is
designed as a general purpose code which addresses problems of astrophysical interest where
the coupling of the radiation field with the fluid flow dominates the structure and 
evolution of the object under consideration.

One of the major difficulties of standard numerical methods is to resolve and to keep track 
of the nonlinear features of the system. They typically appear in spatially very narrow 
regions and introduce multiple length and time scales. 
In order to compute the dynamics of the system properly one therefore needs to resolve
the energetics carefully.

We have implemented an implicit adaptive grid scheme to resolve and track the nonlinear 
features, such as shock waves, ionization fronts, or radiation fronts. 
In \S 2 we briefly review the physics of radiation hydrodynamics and the accompaning
constitutive relations. 
In \S 3 we summarize some numerical details, especially the adaptive grid method, of the 
code and comment on the coding style.
In \S 4 we discuss eight test problems: Noh's shock tube, Woodward's blast wave,
Sedov-Taylor self-similar blast wave; radiative heating and cooling for different ratios
of absorptive to scattering opacity and various transfer schemes; subcritical and 
supercritical shock waves, and a radiative blast wave in a power law atmosphere.
.