Numerical modeling and simulations have been essential for rapid developments of vacuum electronic devices. Pseudospectral solvers have interesting capabilities to be considered, but up to now, they have not been extensively used for the modeling of vacuum tubes. In this paper, we present a novel 1-D time-domain numerical scheme which has the great aptitude of considering geometrical dispersion characteristic of helix traveling-wave tube (TWT) in time domain. This ability is interesting for one-run investigation of time-domain events such as pulse excitation of wideband tubes. The numerical model is extended to have simultaneously arbitrary order of accuracy in space and time derivations; so we achieve a code which presents a very low level of numerical dispersion error, without forcing a notable numerical calculation burden. To validate our new simulation tool, we have studied the experimental results of a TWT product, and successfully compared the results to the impulse response of the new 1-D code.