In this paper the Shortley-Weller finite difference method

applied to the two-point boundary value problems

$-(p(x)u')'=f$ with the Dirichlet boundary condition

is considered. We show several error bounds of the 

Shortley-Weller finite difference solutions in the case 

where $p$ and $f$ have certain regularity

using Yamamoto's explicit inversion formula for 

tridiagonal matrices. We also consider the cases 

where $p$ and $f$ are discontinuous.