The aim of this technical brief is to test numerical inverse Laplace transform methods with application in the framework of the thermal characterization experiment. The objective is to find the most reliable technique in the case of a time resolved experiment based on a thermal disturbance in the form of a periodic function or a distribution. The reliability of methods based on the Fourier series methods is demonstrated.
1.
Maillet
, D.
, André
, S.
, Batsale
, J. -C.
, Degiovanni
, A.
, and Moyne
, C.
, 2000, Thermal Quadrupoles: An Efficient Method for Solving the Heat Equation Through Integral Transforms
, Wiley
, New York
.2.
Davies
, B.
, and Martin
, B.
, 1979, “Numerical Inversion of the Laplace Transform: A Survey and Comparison of Methods
,” J. Comput. Phys.
0021-9991, 33
, pp. 1
–32
.3.
Duffy
, D. G.
, 1993, “On the Numerical Inversion of Laplace Transform: Comparison of Three New Methods on Characteristic Problems From Applications
,” ACM Trans. Math. Softw.
0098-3500, 19
, pp. 333
–359
.4.
de Hoog
, F. R.
, Knight
, J. H.
, and Stokes
, A. N.
, 1982, “An Improved Method for Numerical Inversion of Laplace Transforms
,” SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput.
0196-5204, 3
, pp. 357
–366
.5.
Gaver
, D. P.
, Jr., 1966, “Observing Stochastic Processes, and Approximate Transform Inversion
,” Oper. Res.
0030-364X, 14
, pp. 444
–459
.6.
Stehfest
, H.
, 1970, “Algorithm 368: Numerical Inversion of Laplace Transforms
,” Commun. ACM
0001-0782, 13
, pp. 47
–49
.7.
Den Iseger
, P.
, 2006, “Numerical Transform Inversion Using Gaussian Quadrature
,” Probability in the Engineering and Informational Sciences
, 20
, pp. 1
–44
.8.
Battaglia
, J. -L.
, Kusiak
, A.
, and Batsale
, J. -C.
, 2007, “Thermal Diffusivity Estimation in a Picosecond Photoreflectance Experiment
,” ASME J. Heat Transfer
0022-1481, 129
, pp. 756
–758
.Copyright © 2011
by American Society of Mechanical Engineers
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