I just posted my first blog post, on using BandedMatrices.jl to solve ordinary differential equations via finite differences / spectral methods: https://approximatelyfunctioning.blogspot.com/2018/12/banded-matrices-and-ordinary.html

This is first of a series outlining the results of the NumFocus small development grant to add support for GPUs and other backends to BlockBandedMatrices.jl