
The code cheby is intended to illustrate various Chebyshev spectral methods
(namely Galerkin, tau and collocation) by solving a 1-D second order
differential equation with boundary conditions:

 d^2 u/dx^2 - 4 du/dx + 4 u = e^x + C,          x in [-1,1]

  u(-1) = 0  and u(1) = 0

  C =  - 4 e /(1+e^2)

The exact solution is

 u(x) = e^x - sinh(1)/sinh(2)  e^{2x} + C/4

and is used to measure the accuracy of the numerical solution.

The numerical solution is searched by expansion onto Chebyshev
polynomials T_0(x), T_1(x), ..., T_N(x).

The maximum order of Chebyshev polynomials, N, is set by the
integer variable nn at the first line of cheby.C :

        nn = N + 1

By default nn is set to 5, so that N = 4.

The code cheby produces various output ASCII files to draw
some figures with Grace.

