  In astrophysical regimes where the collisional excitation of hydrogen atoms
is relevant, the cross sections for the interactions of hydrogen atoms with
electrons and protons are necessary for calculating line profiles and
intensities. In particular, at relative velocities exceeding ~1000 km/s,
collisional excitation by protons dominates over that by electrons.
Surprisingly, the hydrogen-proton cross sections at these velocities do not
exist for atomic levels of n >= 4, forcing researchers to utilize extrapolation
via inaccurate scaling laws. In this study, we present a faster and improved
algorithm for computing cross sections for the hydrogen-proton collisional
system, including excitation and charge transfer to the n >= 2 levels of the
hydrogen atom. We develop a code named BDSCx which directly solves the
Schrodinger equation with variable (but non-adaptive) resolution and utilizes a
hybrid spatial-Fourier grid. Our novel hybrid grid reduces the number of grid
points needed from ~4000 n^6 (for a "brute force", Cartesian grid) to ~2000 n^4
and speeds up the computation by a factor ~50 for calculations going up to n =
4 . We present (l,m)-resolved results for charge-transfer and excitation final
states for n = 2--4 and for projectile energies of 5--80 keV, as well as
fitting functions for the cross sections. The ability to accurately compute
proton-hydrogen cross sections to n = 4 allows us to calculate the Balmer
decrement, the ratio of Balmer alpha to Balmer beta line intensities. We find
that the Balmer decrement starts to increase beyond its largely constant value
of 2--3 below 10 keV, reaching values of 4--5 at 5 keV, thus complicating its
use as a diagnostic of dust extinction when fast (~1000$ km/s) shocks are
impinging upon the ambient interstellar medium.
