  In this paper we report and compare the numerical results for an ocean
circulation model obtained by the classical truncated boundary formulation, the
free boundary approach and a quasi-uniform grid treatment of the problem. We
apply a shooting method to the truncated boundary formulation and finite
difference methods to both the free boundary approach and the quasi-uniform
grid treatment. Using the shooting method, supplemented by the Newton's
iterations, we show that the ocean circulation model cannot be considered as a
simple test case. In fact, for this method we are forced to use as initial
iterate a value close to the correct missing initial condition in order to be
able to get a convergent numerical solution. The reported numerical results
allow us to point out how the finite difference method with a quasi-uniform
grid is the less demanding approach and that the free boundary approach
provides a more reliable formulation than the classical truncated boundary
formulation.
