Espectrales

Estructura
Introducción
El sistema de Fourier
Método Espectral Tau
Método de Galerkin
Expansión Discreta de Fourier
Aliasing
Polinomios de Chebyshev
Método de Colocación
⎛
⎜
⎝
T 0 (1) T 1 (1) T 2 (1) T 3 (1) T 4 (1) T 5 (1)
T 0 (x 1 ) T 1 (x 1 ) T 2 (x 1 ) T 3 (x 1 ) T 4 (x 1 ) T 5 (x 1 )
T 0 (x 2 ) T 1 (x 2 ) T 2 (x 2 ) T 3 (x 2 ) T 4 (x 2 ) T 5 (x 2 )
T 0 (x 3 ) T 1 (x 3 ) T 2 (x 3 ) T 3 (x 3 ) T 4 (x 3 ) T 5 (x 3 )
T 0 (x 4 ) T 1 (x 4 ) T 2 (x 4 ) T 3 (x 4 ) T 4 (x 4 ) T 5 (x 4 )
T 0 (−1) T 1 (−1) T 2 (−1) T 3 (−1) T 4 (−1) T 5 (−1)
⎞ ⎡
⎟ ⎢
⎠ ⎣
ó bien, puesto que T n (1) = 1 y T n (−1) = (−1) n para toda n, se tiene
⎛
⎜
⎝
1 1 1 1 1 1
T 0 (x 1 ) T 1 (x 1 ) T 2 (x 1 ) T 3 (x 1 ) T 4 (x 1 ) T 5 (x 1 )
T 0 (x 2 ) T 1 (x 2 ) T 2 (x 2 ) T 3 (x 2 ) T 4 (x 2 ) T 5 (x 2 )
T 0 (x 3 ) T 1 (x 3 ) T 2 (x 3 ) T 3 (x 3 ) T 4 (x 3 ) T 5 (x 3 )
T 0 (x 4 ) T 1 (x 4 ) T 2 (x 4 ) T 3 (x 4 ) T 4 (x 4 ) T 5 (x 4 )
1 −1 1 −1 1 −1
⎞ ⎡
⎟ ⎢
⎠ ⎣
a 0
a 1
a 2
a 3
a 4
a 5
⎤
a 0
a 1
a 2
a 3
a 4
a 5
⎤
=
⎥ ⎢
⎦ ⎣
⎡
=
⎥ ⎢
⎦ ⎣
⎡
F 2
f (x 1 )
f (x 2 )
f (x 3 )
f (x 4 )
F 1
F 2
f (x
f (x
f (x
f (x
F 1
⎤
⎥
⎦
Ricardo Becerril Bárcenas
Una breve introducción a los Métodos Espectrales