WOLFRAM|DEMONSTRATIONS PROJECT

Chebyshev Spectral Differentiation via Fast Fourier Transform

​
-t
2
+4t+5
4-2t
error in -t
2
+4t+5
sum of error square vs. N
interior points
10
□
□
□
□
□
□
□
□
□
□
□
□
-1.0
-0.5
0.0
0.5
1.0
-2
-1
0
1
x
f(x)

Consider the function
f(x)=sin(5x)e
x
with derivative
f'(x)=sin(5x)e
x
+5cos(5x)e
x
. 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
.