Summary form only given. The authors discussed the application of Fourier transform, finite difference, finite element, real space, multioperator, and Lanczos approaches to paraxial electric field propagation problems in guided-wave optics. Although these methods are generally applied to the Fresnel equation, the authors also considered a class of solution algorithms for wide-angle equations. The results of these techniques were employed to estimate the accuracy of the Fresnel in guided-wave contexts for both continuous and discontinuous refractive index profiles. The relative advantages and disadvantages of the various methods with regard to either numerical convergence or computation time were examined. Reflection at an inhomogeneous dielectric interface was also considered. The computational formalisms were illustrated for integrated optic microlenses and semiconductor rib waveguide bends and Y-junctions both numerically and by direct comparison with experiment. >