Chapter 37: Pseudospectral Methods

For PDEs with periodic boundary conditions, sometimes it is advantageous to use spectral methods for the solution. There are a few ways to utilize spectral methods; however in this chapter only one method will be presented, namely, the pseudospectral method. For this method, the basic strategy is similar to the finite difference approach, but the means by which the spatial derivatives are computed is different. For the spectral method, the Fourier transform is used to transform a function into spectral space, and the spatial derivative is calculated in spectral space, where it is a simple operation. The result is then transformed back into real space.