Polynomial supd(2) Lie algebra techniques in solving the second-harmonic generation model: comparison of exact and approximate calculations

We compare exact and SU(2)-cluster approximate calculation schemes to determine dynamics of the second-harmonic generation model using its reformulation in terms of the polynomial Lie algebra supd(2). These schemes, based on diagonal representations of the model evolution operator (due to diagonalizing the model Hamiltonian) and realized in the algorithmic forms, enabled us to implement computer experiments exhibiting a satisfactory accuracy of the cluster approximations in a large range of characteristic model parameters.