Mapped grid methods for Numerov propagation

The Computational toll of solving the Schroedinger equation for certain atomic systems is sometimes prohibitively heavy. We present a grid-mapping method which decreases the number of points needed, and at the same time maintains or increases accuracy for three-atom scattering. By developing a hyperspherical mapping method for Numerov propagation, scattering cross-sections can be found for a large range of energies. This method is useful for systems with very shallow bound states where the mapping will give a large number of data points inside the potential well while decreasing the number of points at a large hyper-radius. The change in grid sizes is controlled by a mapping function that is easily modified. Results are shown for scattering in the HeH$_{\mathrm{2}}$ and HNe$_{\mathrm{2}}$ systems.