Generalized Laguerre Spectral Method for Ordinary Differential Equation

Abstract

In this paper, we propose generalized Laguerre spectral method for two order ordinary differential equation base on modified generalized Laguerre 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.