  We present the numerical simulations of winds from evolved giant stars using
a fully non-linear, time dependent 2.5-dimensional magnetohydrodynamic (MHD)
code. This study extends our previous fully non-linear MHD wind simulations to
include a broadband frequency spectrum of Alfv\'en waves that drive winds from
red giant stars. We calculated four Alfv\'en wind models that cover the whole
range of Alfv\'en wave frequency spectrum to characterize the role of freely
propagated and reflected Alfv\'en waves in the gravitationally stratified
atmosphere of a late-type giant star. Our simulations demonstrate that, unlike
linear Alfv\'en wave-driven wind models, a stellar wind model based on plasma
acceleration due to broadband non-linear Alfv\'en waves, can consistently
reproduce the wide range of observed radial velocity profiles of the winds,
their terminal velocities and the observed mass loss rates. Comparison of the
calculated mass loss rates with the empirically determined mass loss rate for
alpha Tau suggests an anisotropic and time-dependent nature of stellar winds
from evolved giants.
