  Finite difference methods are traditionally used for modelling the time
domain in numerical weather prediction (NWP). Time-spectral solution is an
attractive alternative for reasons of accuracy and efficiency and because time
step limitations associated with causal, CFL-like critera are avoided. In this
work, the Lorenz 1984 chaotic equations are solved using the time-spectral
algorithm GWRM. Comparisons of accuracy and efficiency are carried out for both
explicit and implicit time-stepping algorithms. It is found that the efficiency
of the GWRM compares well with these methods, in particular at high accuracy.
For perturbative scenarios, the GWRM was found to be as much as four times
faster than the finite difference methods. A primary reason is that the GWRM
time intervals typically are two orders of magnitude larger than those of the
finite difference methods. The GWRM has the additional advantage to produce
analytical solutions in the form of Chebyshev series expansions. The results
are encouraging for pursuing further studies, including spatial dependence, of
the relevance of time-spectral methods for NWP modelling.
