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Notes
These are a collection of personal notes on mathematical topics that I have encountered. They are not peer-reviewed and may contain errors. If you find any, please let me know!
Tau-methods
(updated 1 Sep 2023)
The tau-method is an extensive technique for enforcing very general boundary conditions as well as continuity across cells in numerical methods. It is the technique employed by Dedalus, a parallelised software for spectral methods, and is implicitly utilized in the ultraspherical method of Olver and Townsend. In these notes we give a numerical linear algebra perspective on how to implement a tau-method which may be helpful for beginners to build an intuition.