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We investigate the use of parabolic equation (PE) methods for solving radio-wave propagation in polar ice. PE methods provide an approximate solution to Maxwell's equations, in contrast to full-field solutions such as finite-difference-time-domain (FDTD) methods, yet provide a more complete model of propagation than simple geometric ray-tracing (RT) methods that are the current state of the art for simulating in-ice radio detection of neutrino-induced cascades. PE are more computationally efficient than FDTD methods, and more flexible than RT methods, allowing for the inclusion of diffractive effects, and modeling of propagation in regions that cannot be modeled with geometric methods. We present a new PE approximation suited to the in-ice case. We conclude that current ray-tracing methods may be too simplistic in their treatment of ice properties, and their continued use could overestimate experimental sensitivity for in-ice neutrino detection experiments. We discuss the implications for current in-ice Askaryan-type detectors and for the upcoming Radar Echo Telescope; two families of experiments for which these results are most relevant. We suggest that PE methods be investigated further for in-ice radio applications.