Page 15 - Laplace transform numerical inversion
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Bruno Josso & Leif Larsen: Laplace transform numerical inversion - June 2012 -
p 13
2
3
4
5
6
-0.5
0
1
0
0.5
0
1
2
3
4
5
6
-0.001
-0.0005
0
0.0005
0.001
Error: f(t) - Fp_inv(t)
Test: Fp_inv(t) < 0
Figure 10: Inversion of
f
(
t
) =
e
−
µt
by Legendre (
K
= 20
) algorithm.
2
3
4
5
6
-0.5
0
1
0
0.5
1
1.5
2
Fp_inv(t)
f(t)
0
1
2
3
4
5
6
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
Error: f(t) - Fp_inv(t)
Test: Fp_inv(t) < 0
Chebyshev inverse Laplace transform
Figure 11: Inversion of
f
(
t
) =
e
−
µt
by Chebyshev (
K
= 20
) algorithm.
2
3
4
5
6
-0.5
0
1
0
0.5
1
1.5
2
0
1
2
3
4
5
6
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
Fp_inv(t)
f(t)
Error: f(t) - Fp_inv(t)
Test: Fp_inv(t) < 0
Laguerre inverse Laplace transform
Figure 12: Inversion of
f
(
t
) =
e
−
µt
by Laguerre (
K
= 17
) algorithm.
