This investigation presents a spectral method for solving the one-dime
nsional shallow-water wave equations. The spectral method is based on
the Chebyshev collocation technique and finite-difference time steppin
g. The spectral method and finite-difference Preissmann scheme are app
lied to route a log-Pearson Type III hydrograph through a wide rectang
ular channel, and the results are compared. The spectral method perfor
ms better than the Preissmann scheme as long as the time-stepping erro
rs are kept low. However, for larger time steps, the Preissmann scheme
, which is almost second-order accurate in time (and second-order accu
rate in space) performs better than the spectral scheme, which is firs
t-order accurate in time and has so-called infinite-order accuracy in
space. This seems to indicate that the order of accuracy in time discr
etization is more important than that in space discretization? in nume
rical models, for fast-rising floods and friction-dominated flows.