Pseudo-spectral method

Summary

A pseudo-spectral method is a spectral method that imposes the equation at grid points, by collocation. It does not use integrals against the basis functions. Derivatives are computed in coefficient space, for example with the fast Fourier transform, while products and other nonlinear terms are computed pointwise on the grid. This keeps the accuracy of spectral methods at a much lower cost for nonlinear problems. The price is aliasing errors from the pointwise products, which are often removed by padding or truncation. See the definition.