Generalized Laguerre Interpolation and its Application to Differential Equation

In this paper, we develop the generalized Laguerre pseudospectral method for solving initial problems of second order ordinary differential equation. We also propose a multi-step version of the generalized Laguerre collocation method, which are very efficient for long-time numerical simulations. The numerical solutions possess the spectral accuracy. The global convergence of proposed algorithms are proved. Numerical results demonstrate the effectiveness of proposed methods and coincide well with theoretical analysis.