An article describing Chebfun's discretizations of ODE boundary-value problems has been published in the Education section of SIAM Review: J. L. Aurentz and L. N. Trefethen, Block operators and spectral discretizations, SIAM Review 59 (2017), pp. 423-446. The article presents a sequence of 12 examples illustrating how such problems can be solved with the codes diffmat, intmat, diffrow, introw, cumsummat, and gridsample. Chebfun uses the same vectors and matrices constructed by these codes wrapped up in an automatic grid-refinement scheme. See