  The Szymanzik improvement program for gauge theories is most commonly
implemented using forward finite difference corrections to the Wilson action.
Central symmetric schemes naively applied, suffer from a doubling of degrees of
freedom, identical to the well known fermion doubling phenomenon. And while
adding a complex Wilson term remedies the problem for fermions, it does not
easily transfer to real-valued gauge fields. In this talk I report on recent
progress in formulating symmetric discretization schemes for classical actions
of simple one-dimensional problems. They avoid doubling by exploiting the weak
imposition of initial/boundary conditions. Inspired by recent work in the field
of numerical analysis of partial differential equations, I construct a
regularized summation-by-parts finite difference operator using boundary data
based on affine coordinates. Application to a classical initial value problems
with second order derivatives are presented.
