Details

In the discrete Chebyshev–Gauss–Lobatto case, the interior points are given by . These points are the extrema of the Chebyshev polynomials of the first kind, .

The Chebyshev derivative matrix at the quadrature points is an matrix given by

, , for , and for , , and ,

where for and .

The matrix is then used as follows: and , where is a vector formed by evaluating at , , and and are the approximations of and at the .

References

[1] P. Moin, Fundamentals of Engineering Numerical Analysis, Cambridge, UK: Cambridge University Press, 2001.

[2] L. N. Trefethen, Spectral Methods in MATLAB, Philadelphia: SIAM, 2000.

[3] J. Crank, The Mathematics of Diffusion, 2nd ed., New York: Oxford University Press, 1975.