Abstract
It is shown that spectral and pseudospectral methods can lead to great savings in numerical efficiency-typically, at least a factor of four in storage and eight in operation count-in comparison with finite-difference methods for solving eigenvalue and nonseparable, noniterative boundary value problems at the cost of only a a slight amount of additional programming. The special problems or apparent problems that geophysical boundary layers, critical latitudes and critical levels and real data create for spectral algorithms are also discussed along with when and how these can be solved.
