Generalized Laguerre pseudospectral method based Laguerre interpolation

In this paper, we develop the generalized Laguerre pseudospectral method for the second-order ordinary differential equation based on the modified generalized Laguerre approximation, which is very efficient for the long-time numerical simulations of dynamical systems. The numerical solution possesses the spectral accuracy. The global convergence of the proposed algorithm is proved. Numerical results demonstrate the effectiveness of the proposed method and coincide well with theoretical analysis.