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The recent identification of the driving mechanism responsible for the slowly pulsating B stars (and, by inference, the line-profile variables farther up the main sequence) has renewed an interest in finding accurate, numerical solutions of the stellar pulsation equations that can be compared with observation. These variable stars have a wide range of rotation rates and, moreover, the g-mode instabilities belong to high radial order, factors which make numerical calculations extremely difficult even in the linear, adiabatic limit. This paper is a progress report on efforts to develop a robust numerical scheme for computing numerical eigenmodes of arbitrary order and for arbitrary rotation rate. Some success has been achieved by generalizing to two dimensions the standard technique for calculating the nonradial modes of spherical stellar models. The third dimension (or the longitudinal dependence) is removed from the problem by imposing an exp($im\phi$) behavior. The three dependent variables are the radial and latitudinal components of the displacement together with the pressure perturbation, all evaluated on level surfaces and normalized to have nonzero values on the four boundaries. The integration in polar angle is carried out simultaneously with the inward and outward radial integrations and the fitting at an intermediate point determines the unknown boundary displacements as well as the eigenvalue. The results of some preliminary mode calculations will be presented and compared with earlier variational solutions.
