Algorithm / Implementation of PDE15s

[Samuel Morgenstern]

Hello,

I was wondering if anyone had any details on the algorithm on the backend of PDE15s. I know that it is using, and I suspect it is implementing spectral collocation for the spatial discretization, but I wanted to see if anyone could confirm this.

Best,

Sam

[Nick Trefethen]

Sam - I think there's no publication, as summarized in the paragraph below from Appendix A of Exploring ODEs, which is freely available online at https://people.maths.ox.ac.uk/trefethen/ExplODE/.  Perhaps Nick Hale will be able to tell you more.  - Nick Trefethen

[Nick Hale]

Hi all

Yes, that about summarises it. 

A few extra details are that: (a) it  'chunks' time steps and does spatial 

adativity between these using the standard Chebfun 'happiness' check 

on the tail of the Chebyshev/Fourier coefficients and (b) boundary conditions 

(in the nonperiodic case) are enforced by solving the ODE system in time 

as DAEs with rectangular projection and a singular mass matrix (see 

Driscoll and Hale, IMAJNA, 2015, Section 6.2).

Best regards

Nick

[Samuel Morgenstern]

Thank you!