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

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

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.

u(y)=cos(5y)-15

2

y

u(y)

This Demonstration plots , , and , as well as the error made if the first- and second-order derivatives of are approximated using Chebyshev–Gauss–Lobatto points.

u(y)

u'(y)

u''(y)

u(y)

As you increase the number of interior points , you can see how the error (e.g., for given by ) becomes insignificant.

N

u'

u'()-

y

i

u'

i,approximate