  We develop some calculation schemes to determine dynamics of a wide class of
integrable quantum-optical models using their symmetry adapted reformulation in
terms of polynomial Lie algebras $su_{pd}(2)$. These schemes, based on
"diagonal" representations of model evolution operators (via diagonalizing
Hamiltonians with the help of the $su_{pd}(2)$ defining relations), are
implemented in the form adapted for numerical calculations. Their efficiency is
demonstrated on the example of the second-harmonic-generation model.
