  To facilitate the numerical analysis of particle methods, we derive
truncation error estimates for the approximate operators in a generalized
particle method. Here, a generalized particle method is defined as a meshfree
numerical method that typically includes other conventional particle methods,
such as smoothed particle hydrodynamics or moving particle semi-implicit
methods. A new regularity of discrete parameters is proposed via two new
indicators based on the Voronoi decomposition of the domain along with two
hypotheses of reference weight functions. Then, truncation error estimates are
derived for an interpolant, approximate gradient operator, and approximate
Laplace operator in the generalized particle method. The convergence rates for
these estimates are determined based on the frequency with which they appear in
the regularity and hypotheses. Finally, the estimates are computed numerically
and the results are shown to be in good agreement with the theoretical results.
