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Page 715 of Mathematical Reviews Vol. 38, Issue 4 [page]

1969 Mathematical Reviews  
.; Abate, J. 4029 Numerical inversion of Laplace transforms by relating them to the finite Fourier cosine transform. J. Assoc. Comput. Mach. 15 (1968), 115-123.  ...  Authors’ summary: “In this paper the problem of readily determining the inverse Laplace transform numerically by a method which meets the efficiency requirements of automatic digital computation is discussed  ... 

An analytical model for simulating two-dimensional multispecies plume migration

Jui-Sheng Chen, Ching-Ping Liang, Chen-Wuing Liu, Loretta Y. Li
2016 Hydrology and Earth System Sciences  
Generalized analytical solutions in compact format are derived through the sequential application of the Laplace, finite Fourier cosine, and generalized integral transform to reduce the coupled partial  ...  The system of algebraic equations is next solved for each species in the transformed domain, and the solutions in the original domain are then obtained through consecutive integral transform inversions  ...  The authors are grateful to the Ministry of Science and Technology, Republic of China, for financial support of this research under contract MOST 103-2221-E-0008-100.  ... 
doi:10.5194/hess-20-733-2016 fatcat:u5c62aignrd6pehlzpqpboh75u

Peaks and jumps reconstruction with B-splines scaling functions [article]

Luis Ortiz-Gracia, Josep J. Masdemont
2013 arXiv   pre-print
We consider a methodology based in B-splines scaling functions to numerically invert Fourier or Laplace transforms of functions in the space L^2(R).  ...  The original function is approximated by a finite combination of j^th order B-splines basis functions and we provide analytical expressions for the recovered coefficients.  ...  Acknowledgements This work has been partially supported by the grants SGR2009-859, MTM2009-06973 and MTM2012-31714.  ... 
arXiv:1302.1374v1 fatcat:meas4s5rfvhnxfldo4kkdyrjni

The Noise Handling Properties of the Talbot Algorithm for Numerically Inverting the Laplace Transform [article]

Colin L. Defreitas, Steve.J.Kane
2017 arXiv   pre-print
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, the regularization properties are evaluated through a series of standard test functions in which noise is added to the inverse transform.  ...  Since the Laplace Transform is closely related to the Fourier transform it is not surprising that inversion methods based on a Fourier series expansion would yield accurate results.  ... 
arXiv:1703.02857v1 fatcat:5tywbth2qvcfjpgdldb2rwxzne

A new method for non-Fourier thermal response in a single layer skin tissue

Balaram Kundu, Debojit Dewanjee
2015 Case Studies in Thermal Engineering  
The non-Fourier and Fourier thermal responses in one-dimensional single layer skin tissue under selective boundary conditions are investigated by applying the Laplace Transformation method (LTM).  ...  The present method accurately describes the deviation of the temperature response of the non-Fourier model from the Fourier model and roles of important physiological parameters.  ...  The solutions of Eq. (5) subjected to respective boundary conditions transformed in the Laplace domain are obtained by their inversion to t-domain by employing inverse theorem for Laplace transformation  ... 
doi:10.1016/j.csite.2015.02.001 fatcat:uviogm54efgsfo6oin4xzoiqqa

The summation of power series and Fourier series

I.M. Longman
1985 Journal of Computational and Applied Mathematics  
It is assumed that the coefficients of the series are given analytically, and then the numerator of the integrand is determined by the aid of the inverse of the two-sided Laplace transform, while the denominator  ...  Since Fourier series can be expressed in terms of power series, the method is applicable also to them.  ...  In order to make use of the elaborate machinery of the two-sided Laplace transform [lo], we now write the moments pk in the form &ll,=h(p), p=k=l,2,3 ).._) to emphasise the fact that we now regard them  ... 
doi:10.1016/0377-0427(85)90038-x fatcat:dg2txz6f7zhgrnsxpvpotrf3aa

A bibliography on numerical inversion of the Laplace transform and applications

Robert Piessens
1975 Journal of Computational and Applied Mathematics  
Note on an inversion formula for the Laplace transformation.  ...  Numerical inversion of Laplace transforms by relating them to the finite Fourier Cosine trans- form. J. ACM 1__5 (19687, 115-123. 8. Fahidy, T. Z.  ...  The fast Fourier transform algorithm : Program- ming considerations in the calculation of sine, cosine and Laplace transforms. J. Sound Vib. 1_22 (1970), 315-337. 4. Cost, T. L.; Becker, E. B.  ... 
doi:10.1016/0771-050x(75)90029-7 fatcat:4fuuh73swngqlcdidym4incf4q

Page 36 of Journal of Thermophysics and Heat Transfer Vol. 2, Issue 1 [page]

1988 Journal of Thermophysics and Heat Transfer  
Dubner, W.M. and Abate, J., “‘Numerical Inversion of Laplace Transforms by Relating Them to the Finite Fourier Cosine Trans- form,’’ Journal of the ACM, Vol. 15, Jan. 1968, pp. 115-123. 20Durbin, F., “  ...  ‘Numerical Inversion of Laplace Transforms: Effi- cient Improvement to Dubner and Abate’s Method,’’ The Computer Journal, Vol. 17, June 1973, pp. 371-376. 21Segerlind, L.J., “‘Applied Finite Element Analysis  ... 

Improved FFT-based numerical inversion of Laplace transforms via fast Hartley transform algorithm

Chyi Hwang, Ming-Jeng Lu, Leang S. Shieh
1991 Computers and Mathematics with Applications  
The disadvantages of numerical inversion of the Laplace transform via the conventional fast Fourier transform (FFT) are identified and an improved method is presented to remedy them.  ...  A new in~ersion formula is derived ruch that N equallyspaced samples of the inverse LapLace trsJmforrn function can be obtained by [m/2]+ 1 sets of N-point complex FFT computations or by m sets of real  ...  Dubner and Abate [18] employed the finite cosine transform f°(t) = T F(a) + Z Re F a + 3---~ cos \--~ j k=l ( 3 ) to approximately invert the transform function F(s).  ... 
doi:10.1016/0898-1221(91)90021-u fatcat:p25hfjg7izapdgs4kif7wyp5n4


Tetsuhiko UEDA, Kenichi SAITOH
2016 Aviation  
Since the aeroelastic system including the effects of unsteady aerodynamics is ordinarily described in the frequency domain, the Inverse Discrete Fourier Transform (IDFT) can be utilized to simulate its  ...  The response caused by the external random noise is calculated through a transfer function first in the frequency domain and then converted to the time domain.  ...  For a continuous signal, the impulsive response function of a system is directly related to the inverse Laplace transform of a transfer function, H(s): G(t) = L -1 [H(s)]. (3) In the Laplace transformed  ... 
doi:10.3846/16487788.2016.1227535 fatcat:igkawjpbrfdqrnmndgnr3wkvnu

The inverse Laplace transform of an exact analytical solution for a BVP in groundwater theory

John M Bownds, Tony A Rizk
1992 Journal of Mathematical Analysis and Applications  
One of the main points is that the problem, if rigorously adhered to, involves an inhomogeneous ordinary differential equation (ODE), which, when solved, must then be inverted from the Laplace transform  ...  Although there are numerical procedures for this inversion, effort has been made to maintain closed form analytical expressions.  ...  Much of the work described in [l] centers on the existence of a Green's function in the doubly transformed space (finite cosine in z composed with Laplace transform in t).  ... 
doi:10.1016/0022-247x(92)90072-l fatcat:pg6o2xhrzbhldei7tyclgtuogi

Peaks and jumps reconstruction with B-splines scaling functions

Luis Ortiz-Gracia, Josep J. Masdemont
2014 Journal of Computational and Applied Mathematics  
We consider a methodology based in B-splines scaling functions to numerically invert Fourier or Laplace transforms.  ...  The methodology is particularly well suited when the original function or its derivatives present peaks or jumps due to discontinuities in the domain.  ...  As it is well known, the Fourier transform is closely related to the Laplace transform for zero value funcions on the negative time axis.  ... 
doi:10.1016/ fatcat:yo3xkrsuobddzcxrhkxf6vnlxq

Thin viscoelastic disc subjected to radial non-stationary loading

Adámek V., Valeš F.
2010 Applied and Computational Mechanics  
Finally, the type of derived functions singularities and possible methods for their inverse Laplace transform are mentioned.  ...  After the derivation of motion equations final form, the method of integral transforms in combination with the Fourier method is used for finding the problem solution.  ...  Acknowledgements This work has been supported by the grant GA CR 101/09/P082 and by the project GA AS CR A200760611.  ... 
doaj:0b4101eae2d64aa5b9978696b0b3a014 fatcat:lgtuqh643vgbjoqmcfvftl3ep4

The prosaic Laplace and Fourier transform

G. A. Smith
1995 AIP Conference Proceedings  
In Electrical Engineering especially, Laplace and Fourier Transforms have been used for a long time as a way to change the solution of differential equations into trivial algebraic manipulations or to  ...  This tutorial paper is a review of Laplace and Fourier Transforms from an applied perspective with an emphasis on engineering applications.  ...  DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government.  ... 
doi:10.1063/1.48047 fatcat:m3dlldxvhra2dgtwuprions5bq

The Fast Fourier Transform and Its Applications

James W. Cooley, Peter A. W. Lewis, Peter D. Welch
1969 IEEE Transactions on Education  
A description of the alogorithm and its programming is given here and followed by a theorem relating its operands, the finite sample sequences, to the continuous functions they often are intended to approximate  ...  The advent of the fast Fourier transform method has greatly extended our ability to implement Fourier methods on digital computers.  ...  The above theorem and computation also show how to compute Laplace transforms by using the Fourier transform.  ... 
doi:10.1109/te.1969.4320436 fatcat:gexufgiivvb3lc4byzukobnqii
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