Laguerre polynomials for infinite-domain spectral elements (Q1116299)

The problem \(-u_{xx}+\lambda^ 2u=f\) with boundary coditions \(u(0)=0\) and \(u_ x\to 0\) as \(x\to \infty\) is considered in a variational formalism and the effect of using Laguerre polynomials is considered. These are used in conjugation with Legendre-type elements and the accuracy of the approximations are considered.