  In this paper, we first analyze the strong and weak convergence of projective
integration methods for multiscale stochastic dynamical systems driven by
$\alpha$-stable processes, which are used to estimate the effect that the fast
components have on slow ones. Then we obtain the $p$th moment error bounds
between the solution of slow component produced by projective integration
method and the solution of effective system with $p \in \left(1,
\alpha\right)$. Finally, we corroborate our analytical results through a
specific numerical example.
