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Waveguides that are composed of electromagnetically coupled optical microcavities [coupled resonator optical waveguides (CROWs)] can be used for light guiding, slowing, and storage. In this paper, we present a 2-D analysis of finite-size straight and curved CROW sections based on a rigorous Muller boundary integral equation method. We study the mechanisms of the coupling of whispering-gallery (WG) mode and guiding light around bends in CROWs composed of both identical and size- mismatched microdisk resonators. Our accurate analysis reveals the differences in WG modes coupling in the vicinity of bends in CROWs composed of optically large and wavelength-scale micro- cavities. We propose and discuss possible ways to design low-loss CROW bends and to reduce bend losses. These include selecting specific bend angles depending on the azimuthal order of the WG mode and tuning the radius of the microdisk positioned at the CROW bend.