Introduction to Spectral Methods for Partial Differential Equations

Introducing spectral methods for solving one-dimensional PDEs with periodic boundary conditions. In particular, the pseudo-spectral method is demonstrated for the one-dimensional wave equation, and the viscous Burgers' equation using Python. Comparison between the spectral method and finite difference method is shown for varying numbers of grid points. Here's a link to the Jupyter notebook. This has been updated (some comments noted a broken link). https://nbviewer.jupyter.org/url/ignite.byu.edu/che541/lectures/spectral_.ipynb More comprehensive notes on both Fourier and Chebyshev pseudospectral methods are at https://ignite.byu.edu/spectral.