Spectral methods for solution of the boundary-layer equations

The basic principles of spectral methods are reviewed, and their application to the two-dimensional incompressible boundary-layer equations is discussed. It is shown that spectral collocation methods provide an accuracy sufficient for engineering applications on extremely coarse grids, and the machine time requirements are small. Although for a given stream-wise discretization, the fully spectral scheme requires more computational effort than the marching scheme, the higher accuracy of the former yields a large net gain in efficiency when considered at equivalent error levels.