Spectral methods using generalized Laguerre functions for second and fourth order problems (Q2407918)

This paper is concerned with spectral methods using generalized Laguerre functions for solving some boundary value problems of second- and fourth-order linear differential equations on the half line. The second-order problems come from second-order elliptic equations under polar (resp. spherical) coordinates in two (resp. three) dimensions. By using generalized Laguerre functions the authors construct some Fourier-like Sobolev orthogonal basis functions and propose Laguerre spectral methods which lead to fully diagonal systems of linear algebraic equations. Detailed error estimates for the numerical solutions are derived which imply the convergence of the Laguerre spectral methods. For each problem, numerical examples are also given and the numerical results confirm the theoretical convergence rate.