We study the interaction between converging the nonlinearities within a tim
e step and time step control, on the accuracy of nonequilibrium radiation d
iffusion calculations. Typically, this type of calculation is performed usi
ng operator-splitting where the nonlinearities are lagged one time step. Th
is method of integrating the nonlinear system results in an "effective" tim
e-step constraint to obtain accuracy. A time-step control that limits the c
hange in dependent variables (usually energy) per time step is used. We inv
estigate the possibility that converging the nonlinearities within a time s
tep may allow significantly larger time-step sizes and improved accuracy as
well. The previously described Jacobian-free Newton-Krylov method (JQSRT 6
3 (1999) 15) is used to converge all nonlinearities within a time step. In
addition, a new time-step control method, based on the hyperbolic model of
a thermal wave (J. Comput. Phys. 152 (1999) 790), is employed. The benefits
and cost of a second-order accurate time step are considered. It is demons
trated that for a chosen accuracy, significant increases in solution effici
ency can be obtained by converging nonlinearities within a time step. (C) 2
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