  The convergence problem for scattering states is studied in detail within the
framework of the Algebraic Model, a representation of the Schrodinger equation
in an L^2 basis. The dynamical equations of this model are reformulated
featuring new "Dynamical Coefficients", which explicitly reveal the potential
effects. A general analysis of the Dynamical Coefficients leads to an optimal
basis yielding well converging, precise and stable results. A set of strategies
for solving the equations for non-optimal bases is formulated based on the
asymptotic behaviour of the Dynamical Coefficients. These strategies are shown
to provide a dramatically improved convergence of the solutions.
