MATLAB implementation of the discretization of PDEs on an infinite line
using hybrid chebyshev functions, along the lines of the method described in:
Miquel & Julien, J. Comput. Phys., 349C (2017).
https://doi.org/10.1016/j.jcp.2017.08.034

-----------------------------------------------------------------------------
Directory:
**********

Appendix C of the article contains a prescription to discretize operators. 
The routines below are implementing the method.

TSbox_SCDmatrices.m returns matrices S, C, D.   (see equations [100])
TSbox_interweave.m interweaves the elementary matrices (see equations [103])
TS_transform and TS_itransform implement the physical to spectral transform,
and back. For now, I have elected to use matlab's DFT as the performance and
flexibility (generalization to higher dimensionality) of the DCT and DST is
disappointing.
TSbox_example_translated_harmonic_well.m exemplifies the use of the routines
above on the example of the translated harmonic well (section 4.1, equation [40])

------------------------------------------------------------------------------

N.B.: Only the transforms for basis [18a] are implemented. The transforms for 
basis [18b] will follow soon. If reliables libraries for DCTs and DSTs appear,
I will include them.

N.B.2: Any suggestions should be sent to the address indicated on:
              www.normalesup.org/~benmiquel/contact_en.html

------------------------------------------------------------------------------

Boulder, August 2017
Ben Miquel.


