An algorithm for the inversion of Laplace transforms using Puiseux expansions

This paper is devoted to designing a practical algorithm to invert the Laplace transform by assuming that the transform possesses the Puiseux expansion at infinity. First, the general asymptotic expansion of the inverse function at zero is derived, which can be used to approximate the inverse functi...

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Bibliographic Details
Published in:Numerical algorithms Vol. 78; no. 1; pp. 107 - 132
Main Authors: Wang, Tongke, Gu, Yuesheng, Zhang, Zhiyue
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2018
Springer Nature B.V
Subjects:
Algebra
Algorithms
Asymptotic series
Computer Science
Infinity
Laplace transforms
Methods
Numeric Computing
Numerical Analysis
Original Paper
Science
Theory of Computation
65D30
65R10
Bromwich integral
Gauss–Kronrod rule
44A10
Inverse Laplace transform
Error estimate
Puiseux expansion
Gauss–Legendre rule
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:This paper is devoted to designing a practical algorithm to invert the Laplace transform by assuming that the transform possesses the Puiseux expansion at infinity. First, the general asymptotic expansion of the inverse function at zero is derived, which can be used to approximate the inverse function when the variable is small. Second, an inversion algorithm is formulated by splitting the Bromwich integral into two parts. One is the main weakly oscillatory part, which is evaluated by a composite Gauss–Legendre rule and its Kronrod extension, and the other is the remaining strongly oscillatory part, which is integrated analytically using the Puiseux expansion of the transform at infinity. Finally, some typical tests show that the algorithm can be used to invert a wide range of Laplace transforms automatically with high accuracy and the output error estimator matches well with the true error.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-017-0369-y