  The main goal of this paper is to investigate the order reduction phenomenon
that appears in the integral deferred correction (InDC) methods based on
implicit-explicit (IMEX) Runge-Kutta (R-K) schemes when applied to a class of
stiff problems characterized by a small positive parameter $\varepsilon$,
called singular perturbation problems (SPPs). In particular, an error analysis
is presented for these implicit-explicit InDC (InDC-IMEX) methods when applied
to SPPs. In our error estimate, we expand the global error in powers of
$\varepsilon$ and show that its coefficients are global errors of the
corresponding method applied to a sequence of differential algebraic systems. A
study of these errors in the expansion yields error bounds and it reveals the
phenomenon of order reduction. In our analysis we assume uniform quadrature
nodes excluding the left-most point in the InDC method and the globally stiffly
accurate property for the IMEX R-K scheme. Numerical results for the Van der
Pol equation and PDE applications are presented to illustrate our theoretical
findings.
