Bruno Josso & Leif Larsen: Laplace transform numerical inversion - June 2012 -
p 9
/
18
2
3
4
5
6
-0.5
0
1
0
0
1
2
3
4
5
6
-4e-005
-2e-005
0
2e-005
4e-005
Error: f(t) - Fp_inv(t)
Test: Fp_inv(t) < 0
Figure 5: Inversion of
f
(
t
) =
e
−
µt
by Stehfest
N
= 16
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
-1.5e-005
-1e-005
-5e-006
0
5e-006
1e-005
1.5e-005
Error: f(t) - Fp_inv(t)
Test: Fp_inv(t) < 0
Stehfest inverse Laplace transform
Figure 6: Inversion of
f
(
t
) =
e
−
µt
by Stehfest
N
= 18
algorithm.
2
3
4
5
6
-0.5
0
1
0
.5
1
1.5
2
Fp_inv(t)
f(t)
0
1
2
3
4
5
6
-0.0001
-5e-005
0
5e-005
0.0001
Error: f(t) - Fp_inv(t)
Test: Fp_inv(t) < 0
Stehfest inverse Laplace transform
Figure 7: Inversion of
f
(
t
) =
e
−
µt
by Stehfest
N
= 20
algorithm.
1...,2,3,4,5,6,7,8,9,10 12,13,14,15,16,17,18,19,20,...21