These are Matlab functions to compute the angular Mathieu functions ce
and se using a direct collocation method (i.e. without computing the
Fourier decomposition of the functions).  There are three layers to
these functions.  The calling hierarchy goes from high (top level) to
low (basic building blocks). 

Lowest:  make_matrix_e(N, q, vn), make_matrix_o(N, q, vn) -- These
create the collocation matrices including BCs.  N is the size of the
matrix, q is the scalar value for which the matrix is created.  vn is
the angle grid, but I only use it to get the point spacing h.  

Mid:  mathieu_a(Ne, q), mathieu_b(Ne, q) -- These return the
eigenvalues (Mathieu characteristic values) for all orders up to Ne
for a scalar q value.  

Mid:  mathieu_ce(Ne,q,v), mathieu_se(Ne,q,v) -- These compute the
Mathieu fcns themselves.  Each function returns a set of values at the
grid points v for all orders up to Ne (that is, the return is a matrix
whose rows corresond to different v and whose columns are different
orders).  The functions are computed for a specific scalar q.

High:  plot_eigs -- This makes the classic plot of the Mathieu
characteristics vs. q, i.e. Figure 28.2.1 on
https://dlmf.nist.gov/28.2

High:  plot_mathieu_ce, plot_mathieu_se -- These make plots of the first
Ne Mathieu functions of a particular type.  The plots are made for a
specific q.

I will add additional test fcns to this repo as I continue working.


SDB, May & June 2025

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

Note added July 2025

I added functions to dump the computed ce and se function
values into a golden value file for use in testing.