Generalized Laguerre pseudospectral method for initial problem of the second-order ordinary differential equation

In this paper, we propose the generalized Laguerre pseudospectral method for the second-order ordinary differential equation, which is very efficient for the long-time numerical simulations of dynamical systems, the new method enlarges the range of the application of collocation method. The global convergence of proposed algorithm is proved. Numerical results demonstrate the spectral accuracy of these new approaches and coincide well with theoretical analysis.