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Chebyshev Spectral Differentiation via Fast Fourier Transform

​
f(t)
′
f
(t)
error in f(t)
sum of error square vs. N
interior points
10
Consider the function
f(x)=sin(5x)
x
e
with derivative
f'(x)=sin(5x)
x
e
+5cos(5x)
x
e
. This Demonstration uses Chebyshev differentiation via Fast Fourier Transform (FFT) [1] to estimate
f'(x)
at the
(N+1)
Chebyshev–Gauss–Lobatto points. You can change the number of interior points,
(N-1)
. The error (i.e., the difference between the exact and approximate values of
f'(x)
) decreases for large values of
N
.
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