  Numerical techniques for discretization of velocity space in continuum
kinetic calculations are described. An efficient spectral collocation method is
developed for the speed coordinate - the radius in velocity space - employing a
novel set of non-classical orthogonal polynomials. For problems in which
Fokker-Planck collisions are included, a common situation in plasma physics, a
procedure is detailed to accurately and efficiently treat the field term in the
collision operator (in the absence of gyrokinetic corrections). When species
with disparate masses are included simultaneously, a careful extrapolation of
the Rosenbluth potentials is performed. The techniques are demonstrated in
neoclassical calculations of the bootstrap current and plasma flows in a
tokamak.
