  We present a new oscillation code, GYRE, which solves the stellar pulsation
equations (both adiabatic and non-adiabatic) using a novel Magnus Multiple
Shooting numerical scheme devised to overcome certain weaknesses of the usual
relaxation and shooting schemes appearing in the literature. The code is
accurate (up to 6th order in the number of grid points), robust, efficiently
makes use of multiple processor cores and/or nodes, and is freely available in
source form for use and distribution. We verify the code against analytic
solutions and results from other oscillation codes, in all cases finding good
agreement. Then, we use the code to explore how the asteroseismic observables
of a 1.5 M_sun star change as it evolves through the red-giant bump.
