  The B-spline Galerkin method is investigated for the simple eigenvalue
problem, $y^{\prime\prime} = -\lambda^2 y$. Special attention is give to
boundary conditions. From this analysis, we propose a stable method for the
Dirac equation and evaluate its accuracy by comparing the computed and exact
R-matrix for a wide range of nuclear charges $Z$ and angular quantum numbers
$\kappa$. No spurious solutions were found and excellent agreement was obtained
for the R-matrix.
