Stable and spectrally accurate numerical methods are constructed on ar
bitrary grids for partial differential equations, These new methods ar
e equivalent to conventional spectral methods but do not rely on speci
fic grid distributions. Specifically, we show how to implement Legendr
e Galerkin, Legendre collocation, and Laguerre Galerkin methodology on
arbitrary grids. (C) 1996 Academic Press, Inc.