  In this paper, we discuss some limitations of the modified equations approach
as a tool for stability analysis for a class of explicit linear schemes to
scalar partial derivative equations. We show that the infinite series obtained
by Fourier transform of the modified equation is not always convergent and that
in the case of divergence, it becomes unrelated to the scheme. Based on these
results, we explain when the stability analysis of a given truncation of a
modified equation may yield a reasonable estimation of a stability condition
for the associated scheme. We illustrate our analysis by some examples of
schemes namely for the heat equation and the transport equation.
