A modification of Talbot's method for the simultaneous approximation of several values of the inverse Laplace transform

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A modification of Talbot's method for the simultaneous approximation of several values of the inverse Laplace transform

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 21 , Issue 4 (December 1995) table of contents

Pages: 347 - 371

Year of Publication: 1995

ISSN:0098-3500

Author

Mariarosaria Rizzardi

Istituto Univ. Navale, Naples, Italy

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 7, Downloads (12 Months): 31, Citation Count: 3

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ABSTRACT

In recent years many results have been obtained in the field of the numerical inversion of Laplace transforms. Among them, a very accurate and general method is due to Talbot: this method approximates the value of the inverse Laplace transform f(t), for t fixed, using the complex values of the Laplace transform F(s) sampled on a suitable contour of the complex plane. On the basis of the interest raised by Talbot's method implementation, the author has been induced to investigate more deeply the possibilities of this method and has been able to generalize Talbot's method, to approximate simultaneously several values of f(t) using the same sampling values of the Laplace transform. In this way, the only unfavorable aspect of the classical Talbot method, that is, that of recomputing all of the samples of F(s) for each t, has been eliminated.

REFERENCES

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	1	MURLI, A. AND RIZZARDI, M. 1983. Sull'implementazione del metodo di Talbot per la inversione numerica della Trasformata di Laplace. Rep. SOFMAT 10.83, Progetto Finalizzato Informatica del CNR, Rome, Italy.
	2	A. Murli , M. Rizzardi, Algorithm 682: Talbot's method of the Laplace inversion problems, ACM Transactions on Mathematical Software (TOMS), v.16 n.2, p.158-168, June 1990 [doi>10.1145/78928.78932]
	3	TALBOT, A. 1979. The accurate numerical inversion of Laplace transforms. J. Inst. Math. Appl. 23.

CITED BY 3

	M. López-Fernández , C. Palencia, On the numerical inversion of the Laplace transform of certain holomorphic mappings, Applied Numerical Mathematics, v.51 n.2-3, p.289-303, November 2004
	Giovanni Capobianco , Dajana Conte, An efficient and fast parallel method for Volterra integral equations of Abel type, Journal of Computational and Applied Mathematics, v.189 n.1, p.481-493, 1 May 2006
	Dajana Conte , Ida Del Prete, Fast collocation methods for Volterra integral equations of convolution type, Journal of Computational and Applied Mathematics, v.196 n.2, p.652-663, 15 November 2006