  We construct a sequence of boundary value problems on compact subsets of
smooth noncompact hyperbolic surfaces of finite area. We prove that the
sesquilinear forms associated to these boundary value problems are stable as
well as consistent at continuous functions which vanish at cusps. We also give
an explicit form for the symbol expansion of the Dirichlet-to-Neumann operator
of a certain Schrodinger operator. The symbols appearing in the expansion of
this Dirichlet-to-Neumann operator can be calculated quickly by a computer
using the formulas we provide in this paper.
