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More on the weeks method for the numerical inversion of the Laplace transform
No full textMost of the numerical methods for the inversion of the Laplace Transform require the values of several incidental parameters. Generally, these parameters are related to the properties of the algorithm and to the analytical properties of the Laplace Transform function F(s). One of the most promising inversion methods, the Weeks methods, computes the inverse function f(t) as a series expansion of Laguerre functions involving two parameters, usually denoted by Ï and b. In this paper we characterize the optimal choice bopt of b, which maximizes the rate of convergence of the series, in terms of the location of the singularities of F(s). © 1988 Springer-Verlag
An Extension of the Henrici Formula for the Laplace Transform Inversion
No full textAbstract. Under certain conditions, starting from the Riemann inversion formula, which gives an explicit representation of the inverse Laplace transform in the complex form, we derive an integral equation, of convolution type, whose solution is the inverse Laplace transform function. This formula can be used if the Laplace transform has a finite number of singularities, located everywhere in the complex plane, and provided that their corresponding residues are known. It only requires the knowledge of the Laplace transform function on the real negative axis. Preliminary numerical experiments illustrating the reliability of the inversion algorithm are described
An Extension of the Henrici Formula for the Laplace Transform Inversion
No full textAbstract. Under certain conditions, starting from the Riemann inversion formula, which gives an explicit representation of the inverse Laplace transform in the complex form, we derive an integral equation, of convolution type, whose solution is the inverse Laplace transform function. This formula can be used if the Laplace transform has a finite number of singularities, located everywhere in the complex plane, and provided that their corresponding residues are known. It only requires the knowledge of the Laplace transform function on the real negative axis. Preliminary numerical experiments illustrating the reliability of the inversion algorithm are described
An Extension of the Henrici Formula for the Laplace Transform Inversion
No full textAbstract. Under certain conditions, starting from the Riemann inversion formula, which gives an explicit representation of the inverse Laplace transform in the complex form, we derive an integral equation, of convolution type, whose solution is the inverse Laplace transform function. This formula can be used if the Laplace transform has a finite number of singularities, located everywhere in the complex plane, and provided that their corresponding residues are known. It only requires the knowledge of the Laplace transform function on the real negative axis. Preliminary numerical experiments illustrating the reliability of the inversion algorithm are described
A Computational algorithm for the real inversion of the Laplace transform function
No full textViene proposto un algoritmo numerico per il calcolo della funzione inversa di una Trasformata di Laplace nel caso reale
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Recent developments related to the numerical inversion of a Laplacetransform function: the real inversion problem
No full textIt is proposed an extension of the Riemann inversion formula that can be used for computing the inverse Laplace function only using real values of the Laplace transfor
Computation of the inverse Laplace Transform based on a Collocation method which uses only real values
Full text linkWe 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
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