scholarly journals Parameter N Analysis on the Rational-Talbot Algorithm for Numerical Inversion of Laplace Transform

2021 ◽  
Vol 31 (2) ◽  
pp. 50-60
Author(s):  
Elisandra Freitas ◽  
George Ricardo Libardi Calixto ◽  
Juciara Alves Ferreira ◽  
Bárbara Denicol do Amaral Rodriguez ◽  
João Francisco Prolo Filho
Keyword(s):  
Laplace Transform ◽  
Free Parameter ◽  
Numerical Results ◽  
Numerical Inversion ◽  
Good Precision ◽  
Trigonometric Functions ◽  
Inversion Process ◽  
Elementary Functions ◽  
Exponential Functions ◽  
The Laplace Transform

This article investigates the numerical inversion of the Laplace Transform by the Rational-Talbot method and analyzes the influence on the variation of the free parameter N established by the technique when applied to certain functions. The set of elementary functions, for which the method is tested, has exponential and oscillatory characteristics. Based on the results obtained, it was concluded that the Rational-Talbot method is e cient for the inversion of decreasing exponential functions. At the same time, to perform the inversion process effectively for trigonometric forms, the algorithm requires a greater amount of terms in the sum. For higher values of N, the technique works well. In fact, this is observed in inverting the functions transform, that combine trigonometric and polynomial factors. The method numerical results have a good precision for the treatment of decreasing exponential functions when multiplied by trigonometric functions.

scholarly journals Numerical inversion of the Laplace transform

1999 ◽  
Vol 110 (23) ◽  
pp. 11176-11186 ◽  
Author(s):  
Bruno Hüpper ◽  
Eli Pollak
Keyword(s):  
Laplace Transform ◽  
Numerical Inversion ◽  
The Laplace Transform

scholarly journals The noise handling properties of the Talbot algorithm for numerically inverting the Laplace transform

2018 ◽  
Vol 13 ◽  
pp. 174830181879706 ◽  
Author(s):  
Colin L Defreitas ◽  
Steve J Kane
Keyword(s):  
Fourier Series ◽  
Laplace Transform ◽  
Noisy Data ◽  
Standard Test ◽  
Numerical Inversion ◽  
Test Functions ◽  
Inversion Algorithm ◽  
Inverse Transform ◽  
Exact Data ◽  
The Laplace Transform

This paper examines the noise handling properties of three of the most widely used algorithms for numerically inverting the Laplace transform. After examining the genesis of the algorithms, their error handling properties are evaluated through a series of standard test functions in which noise is added to the inverse transform. Comparisons are then made with the exact data. Our main finding is that the for “noisy data”, the Talbot inversion algorithm performs with greater accuracy when compared to the Fourier series and Stehfest numerical inversion schemes as they are outlined in this paper.

scholarly journals Computer-Aided Numerical Inversion of Laplace Transform

2000 ◽  
Vol 22 (3) ◽  
pp. 189-213 ◽  
Author(s):  
Umesh Kumar
Keyword(s):  
Laplace Transform ◽  
Probability Density Functions ◽  
Numerical Inversion ◽  
Time Varying ◽  
Inversion Technique ◽  
Computer Aided ◽  
The Laplace Transform ◽  
The Time Domain ◽  
Time Invariant ◽  
Exponential Probability

This paper explores the technique for the computer aided numerical inversion of Laplace transform. The inversion technique is based on the properties of a family of three parameter exponential probability density functions. The only limitation in the technique is the word length of the computer being used. The Laplace transform has been used extensively in the frequency domain solution of linear, lumped time invariant networks but its application to the time domain has been limited, mainly because of the difficulty in finding the necessary poles and residues. The numerical inversion technique mentioned above does away with the poles and residues but uses precomputed numbers to find the time response. This technique is applicable to the solution of partially differentiable equations and certain classes of linear systems with time varying components.

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