  Ab initio calculations of the spin wave stiffness constant $D$ for elemental
Fe and Ni performed by different groups in the past have led to values with a
considerable spread of 50-100 %. We present results for the stiffness constant
$D$ of Fe, Ni, and permalloy Fe$_{0.19}$Ni$_{0.81}$ obtained by three different
approaches: (i) by finding the quadratic term coefficient of the power
expansion of the spin wave energy dispersion, (ii) by a damped real-space
summation of weighted exchange coupling constants, and (iii) by integrating the
appropriate expression in reciprocal space. All approaches are implemented by
means of the same Korringa-Kohn-Rostoker (KKR) Green function formalism. We
demonstrate that if properly converged, all procedures yield comparable values,
with uncertainties of 5-10 % remaining. By a careful analysis of the influence
of various technical parameters we estimate the margin of errors for the
stiffness constants evaluated by different approaches and suggest procedures to
minimize the risk of getting incorrect results.
