Generalized Laguerre function spectral method for second order ordinary differential equation

In this paper,we propose generalized Laguerre function spectral method for second order ordinary differential equation base on modified generalized Laguerre function approximation, which are very efficient for long-time numerical simulations of dynamical systems.The global convergence of proposed algorithms are proved.Numerical results demonstrate the spectral accuracy of these new approaches and coincide well with theoretical analysis.