The main goal of this paper is to investigate the order reduction phenomenonthat appears in the integral deferred correction (InDC) methods based onimplicit-explicit (IMEX) Runge-Kutta (R-K) schemes when applied to a class ofstiff problems characterized by a small positive parameter $\varepsilon$,called singular perturbation problems (SPPs). In particular, an error analysisis presented for these implicit-explicit InDC (InDC-IMEX) methods when appliedto SPPs. In our error estimate, we expand the global error in powers of$\varepsilon$ and show that its coefficients are global errors of thecorresponding method applied to a sequence of differential algebraic systems. Astudy of these errors in the expansion yields error bounds and it reveals thephenomenon of order reduction. In our analysis we assume uniform quadraturenodes excluding the left-most point in the InDC method and the globally stifflyaccurate property for the IMEX R-K scheme. Numerical results for the Van derPol equation and PDE applications are presented to illustrate our theoreticalfindings.
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