# Approximating the Derivatives of a Function Using Chebyshev-Gauss-Lobatto Points

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Consider the function defined by . Using the Chebyshev–Gauss–Lobatto points, it is possible to approximate the values of the two first derivatives of at these points.

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Contributed by: Housam Binous, Brian G. Higgins, and Ahmed Bellagi (March 2013)

Open content licensed under CC BY-NC-SA

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## Details

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

The Chebyshev derivative matrix at the quadrature points , , is 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] S. Biringen and C-Y. Chow, *An Introduction to Computational Fluid Mechanics by Example*, Hoboken, NJ: Wiley, 2011.

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