# Chebyshev Spectral Differentiation via Fast Fourier Transform

Chebyshev Spectral Differentiation via Fast Fourier Transform

Consider the function with derivative . This Demonstration uses Chebyshev differentiation via Fast Fourier Transform (FFT) [1] to estimate at the Chebyshev–Gauss–Lobatto points. You can change the number of interior points, . The error (i.e., the difference between the exact and approximate values of ) decreases for large values of .

f(x)=sin(5x)

x

e

f'(x)=sin(5x)+5cos(5x)

x

e

x

e

f'(x)

(N+1)

(N-1)

f'(x)

N