Second Order Generalized Laguerre Function Approximation and Its Applications to Fourth-Order Differential Equations

Abstract

In this paper, we investigate second-order generalized Laguerre approximation. Various orthogonal projections are established. As an example of their important applications, we propose the spectral scheme for some fourth order differential equations on unbounded domain. their convergence are proved. Numerical results demonstrate the high accuracy of this new spectral method.