A method for the numerical inversion of Laplace transforms
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TLDR
A numerical inversion method for Laplace transforms, based on a Fourier series expansion developed by Durbin [5], is presented in this article, where the disadvantage of the inversion methods of that type, the encountered dependence of discretization and truncation error on the free parameters, is removed by the simultaneous application of a procedure for the reduction of the Discretization error, a method for accelerating the convergence of the Fourier Series and a procedure that computes approximately the "best" choice of the free parameter.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 1984-02-01 and is currently open access. It has received 1044 citations till now. The article focuses on the topics: Post's inversion formula & Inverse Laplace transform.read more
Citations
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The Fourier-series method for inverting transforms of probability distributions
Joseph Abate,Ward Whitt +1 more
TL;DR: This paper reviews the Fourier-series method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions and describes two methods for inverting Laplace transform based on the Post-Widder inversion formula.
Journal ArticleDOI
Fractional order theory of thermoelasticity
TL;DR: In this paper, a new theory of thermoelasticity is derived using the methodology of fractional calculus, and a uniqueness theorem for this model is proved and a variational principle and a reciprocity theorem are derived.
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A half-space problem in the theory of generalized thermoelastic diffusion
Hany H. Sherief,Heba A. Saleh +1 more
TL;DR: In this article, the authors considered the problem of a half-space with a permeating substance in contact with the bounding plane in the context of the theory of generalized thermoelastic diffusion with one relaxation time.
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Fault rupture between dissimilar materials: Ill-posedness, regularization, and slip-pulse response
Alain Cochard,James R. Rice +1 more
TL;DR: In this paper, it was shown that in the unstable range the numerical solutions do not converge through grid size reduction, whereas in the stable range, only dying pulses are then observed.
References
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Numerical Inversion of Laplace Transforms: An Efficient Improvement to Dubner and Abate's Method
TL;DR: An accurate method is presented for the numerical inversion of Laplace transform, which is a natural continuation to Dubner and Abate's method, and the error bound on the inverse f{t) becomes independent of t, instead of being exponential in t.
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Numerical Inversion of Laplace Transforms Using a Fourier Series Approximation
TL;DR: A method is presented for numerically inverting a Laplace transform that requires, in addition to the transform function itself, only sine, cosine, and exponential functions and includes a transformation of the approximating series into one that converges very rapidly.
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Numerical Inversion of Laplace Transforms by Relating Them to the Finite Fourier Cosine Transform
H. Dubner,Joseph Abate +1 more
TL;DR: The problem of readily determining the inverse Laplace transform numerically by a method which meets the efficiency requirements of automatic digital computation is discussed because the result inverse function is given as a Fourier cosine series, the procedure requires only about ten FORTRAN statements.
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Numerical inversion of Laplace transforms with application to percentage labeled mitoses experiments.
TL;DR: An improved version of an algorithm due to Dubner and Abate, for the numerical inversion of Laplace transforms is applied to the estimation of parameters from percentage labeled mitoses (PLM) experiments.
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Stochastic theory of spin depolarization of muons diffusing in the presence of traps
K. W. Kehr,D. Richter,G. Honig +2 more
TL;DR: In this article, the decay of phase coherence of muon spin rotation in the case of diffusion in the presence of traps was studied. But the decay function was not modeled in the frequency domain, but in the time domain.