We develop a numerical algorithm for inverting a Laplace transform (LT), based on Laguerre polynomial series expansion of the inverse function under the assumption that the LT is known on the real axis only. The method belongs to the class of Collocation methods (C-methods), and is applicable when the LT function is regular at infinity. Difficulties associated with these problems are due to their intrinsic ill-posedness. The main contribution of this paper is to provide computable estimates of truncation, discretization, conditioning and roundoff errors introduced by numerical computations. Moreover, we introduce the pseudoaccuracy which will be used by the numerical algorithm in order to provide uniform scaled accuracy of the computed approximation for any x with respect to ex . These estimates are then employed to dynamically truncate the series expansion. In other words, the number of the terms of the series acts like the regularization parameter which provides the trade-off between errors. With the aim to validate the reliability and usability of the algorithm experiments were carried out on several test functions.
Computation of the inverse Laplace Transform based on a Collocation method which uses only real values / Cuomo, S; D'Amore, Luisa; A., Murlii; Rizzardi, M.. - In: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. - ISSN 0377-0427. - STAMPA. - 198:1(2007), pp. 98-115. [10.1016/j.cam.2005.11.017]
Computation of the inverse Laplace Transform based on a Collocation method which uses only real values
Cuomo S;D'AMORE, LUISA;
2007
Abstract
We develop a numerical algorithm for inverting a Laplace transform (LT), based on Laguerre polynomial series expansion of the inverse function under the assumption that the LT is known on the real axis only. The method belongs to the class of Collocation methods (C-methods), and is applicable when the LT function is regular at infinity. Difficulties associated with these problems are due to their intrinsic ill-posedness. The main contribution of this paper is to provide computable estimates of truncation, discretization, conditioning and roundoff errors introduced by numerical computations. Moreover, we introduce the pseudoaccuracy which will be used by the numerical algorithm in order to provide uniform scaled accuracy of the computed approximation for any x with respect to ex . These estimates are then employed to dynamically truncate the series expansion. In other words, the number of the terms of the series acts like the regularization parameter which provides the trade-off between errors. With the aim to validate the reliability and usability of the algorithm experiments were carried out on several test functions.File | Dimensione | Formato | |
---|---|---|---|
Computation_cuomo_2007.pdf
accesso aperto
Tipologia:
Altro materiale allegato
Licenza:
Accesso privato/ristretto
Dimensione
333.53 kB
Formato
Adobe PDF
|
333.53 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.